This question is asked for sever reasons, amongst them are the differing claims of Muslim women that is a choice, and a requirement. If it is required why would some make the claim. This must be examined.
Womens’ magazine Cosmopolitan decided it was important to ask this question on July 4, 2016:
While Islam as a religion often comes under heavy scrutiny for its oppression of women, given many wear a hijab around their face or a burqa to cover their full body, isn't it worth hearing how the women themselves feel?
We think so, which is why this Reddit thread, which invites women who do wear a traditional garments to cover themselves up either fully or partially in public, was so interesting to read. How does it feel to wear it? Is it a choice or is there pressure from within their family or their community? Do they feel sidelined in public because of their burqa?
Sadly, this article talks about how a woman feels, addresses the head scarf (hijab) only as a family tradition, but never explores if it is required by Islam. It is as if the brief article asks the question fairly from women who like and hate the hijab. In this it appears unbiased, unless you ask why they addressed the question about pressure from a family versus a religious requirement. The article in truth never addresses who or what places the requirement on the family. Is it not Islam that places this requirement or choice on a family? What does Islam say about the Hijab? Is it a choice?
The Quran states in 33:59 that Muslim men must tell their wives and daughters to cover-up for their own safety. Below is the verse. The reasoning for covering pretty much mean if you do not obey a severe punishment follows.
O Prophet, tell your wives and your daughters and the women of the believers to bring down over themselves [part] of their outer garments. That is more suitable that they will be known and not be abused. And ever is Allah Forgiving and Merciful.
This is not clearly stating to cover the hair. But notice the reasoning behind it. If they are not covered, they will be abused. This a reference to sexual abuse. Who would do the abusing? Considering this passage was given inside an Islamic community, it would be Muslim men doing the abuse. This included daughters. So little girls also had to be cautious of men seeking to sexually abuse them AND WERE TOLD TO COVER THEMSELVES TO KEEP FROM BEING MOLESTED.
The Quran also says in 24:31:
And tell the believing women to reduce [some] of their vision and guard their private parts and not expose their adornment except that which [necessarily] appears thereof and to wrap [a portion of] their headcovers over their chests and not expose their adornment except to their husbands, their fathers, their husbands' fathers, their sons, their husbands' sons, their brothers, their brothers' sons, their sisters' sons, their women, that which their right hands possess, or those male attendants having no physical desire, or children who are not yet aware of the private aspects of women. And let them not stamp their feet to make known what they conceal of their adornment. And turn to Allah in repentance, all of you, O believers, that you might succeed.
Some say this stomping was to show cleavage that their garments did not cover, but the shawl/ head gear draped over them to provide extra protection. Some say that it is indeed a covering over the hair because ‘adornment’ is a direct reference to the hair. A slight reference is made to women stomping so they could show someone their pretty hair, by causing their cover to slip. This has evolved to a tight wrap of the hair not allowing any of it to appear in public. Does this seem optional? Is there a choice given? Remember the statement the above citation states the purpose is to protect the women and daughters from sexual attacks.
In the Islamic countries like Pakistan the head covering of a hijab can also be a chador. One official in the Haripur district of Pakistan in September of 2019, made it mandatory for all school age girls to wear a head covering and gown to dress "in order to protect them from any unethical incident," and “necessary to protect girl students from a growing number of complaints of eve-teasing and harassment."
Here they are saying that school girls’ (ages 5 to 18) hair is tempting men to sexually molest girls, so it is their fault if this happens, IF THEY ARE NOT COVERED. Of course, if they are, their word only counts as half a man in a court of law so they can never bring charges against their molester.
The question of whether the hijab is mandatory has been a central theme wherever Islam wanders today. On August 7, 2019, Al-Qaeda's Al-Sahab media wing released a video of Al-Qaeda leader Ayman Al-Zawahiri titled "The Battle of the Hijab.” The Middle East Media Research Institute caught this, translated it and released a summary of it to the public within a week. According to this lover of shariah, western countries are doing everything they can to destroy Islamic women’s modesty and morals. This is how Islamic women are warned against Western cultural values. It is deemed as an attack on their modesty.
France has had a law forbidding the displaying of religion for a hundred years. It is called, Laïcité (Lah-Cee-Tay). They have been fighting to keep French culture which a hijrah is working to dismiss. France passed a law in 2010 to ban the face veil as part of keeping French culture and Laïcité. Granted this is not about the hijab, but this is a more restrictive requirement placed on Islamic women by stricter observance of Islam seen in many Islamic countries.
This law passed the French Senate with 46 votes and had already passed the upper house of the parliament in July of that year. Justice Minister, Michèle Alliot-Marie stated, “the full veil dissolves a person's identity in that of a community. It calls into question the French model of integration, founded on the acceptance of our society's values. Living with one's face uncovered was a question of dignity and equality."
In the USA the Democratic Party took it upon themselves to lift a 181 year old law forbidding hats in the House of Representatives so that Ilhan Omar would not have to remove her hijab in order to serve in her role as a representative of Minnesota. While a hijab is not a hat it is a head covering. She is one of two Muslim women elected. Rep. Rashida Tlaib does not wear a hijab, so they simply could have enforced the rule showing that not all Muslims follow this rule. Rep. Ilhan Omar has made bold statements about her hijab and her reasons for wearing it. In March 0f 2019, she told Vogue magazine, that
wearing her hijab allows her to be a ‘walking billboard’ not only for her faith but also for representing something different from the norm. ‘To me, the hijab means power, liberation, beauty, and resistance.’
This is the same rule that several Democrats violated, by wearing hoodies on March 28th, 2012, when trying to show they were standing with Trayvon Martin who was killed in Florida.
In 2007, Quebec Canada’s Bouchard-Taylor Com-mission created recommendations, which became policies for the province. Amongst them was:
Judges, Crown prosecutors, police officers, prison guards and the president and vice-president of the National Assembly be prohibited from wearing religious signs.
This recommendation was for government employees alone. It in effect banned the Christians from wearing of a cross, the Sikhs from wearing a turban, Jew from wearing yarmulkes, or Muslim women from wearing a hijab to work in a government post. There is no religious prejudice involved as it does not address any one religion.
Tarek Fatah, a Canadian Muslim “reformist” sees the hijab a little differently than many do today. He wrote of it:
The fact is that while the Sikh turban, Jewish yarmulkes and the Catholic crucifix are definitely religious symbols, the hijab is not. Rather it is a political symbol that until the late 1970s was unheard of in Pakistan, India, Indonesia, Bangladesh, Turkey, Somalia and Nigeria. It was the uniform of the Muslim Brotherhood in the Arab world.
Fatah also made mention of Ferid Chikhi who lives in Qubec and agrees with him that the hijab is a political symbol more than a religious one. Chiki stated,
… the hijab, conceals in itself the idea, the representation or the thought of a first generic sense which is ignored by all and which conveys a double meaning: translated in French or in other languages, this word wants say curtain, separation, hanging ... or even storefront and not dress or scarf that covers the head of women. He simply referred to a separation of the space into two, the foreign men to the Prophet's house and that of his women.
Then, history reminds us, after the death of the Prophet, the male power extended the territory hijab imposing it as a separation between the spaces of all men and all women. Finally, at those generally Islamic and not Muslims, citing verses al-Ahzâb (33 e sura), the khimar is a shawl and djilbab or thaûb are shawls, worn by the women of the time in these same Arab Gulf coun-tries. They did not have the function of covering as they would like to make us believe the head, but the shoulders and the chest.
This is the reason why some ambiguity exists as to whether a hijab is required or not. The Quran refers to covering. It refers to shawls and more. But the specific item of a hijab is not mentioned. It is why Iran has a chador and not a hijab.
Whether required a woman is often left without a choice to wear the hijab. Youness Moussaid, left little doubt of this December 6, 2019 in Bismark, North Dakota, when school officials reported the abuse he had done to his step-daughter. His step-daughter was refusing to wear the hijab and dresses when at school. She snuck in a change of clothing.
Moussaid in response struck the teenage girl with a broom stick, causing bruising on the top of her right hand and on the front of her thighs. He grabbed her hair and struck her head against the wall, causing a quarter-sized bump.
Moussaid admitted to this crime. Perhaps he did not see it as a crime, or did not understand females are considered equals under the law.
The girl now has an order of protection from her step-father. He faces 5 years if convicted. Moussaid felt justified by the Islamic social norm he believed exists to demand his daughter wear a hijab.
 Harvey-Jenner, Catronia. 2016. "Muslim women explain how they feel about wearing a hijab: Mainly it's their choice." Cosmopolitan. July 4. https://www.cosmopolitan.com/uk/reports/news/a44416/muslim-women-explain-how-feel-wearing-burqa-hijab/.
 Davies, Lizzy. 2010. "France: Senate votes for Muslim face veil ban." The Guardian. September 14. Accessed October 1, 2019. https://www.theguardian.com/world/2010/sep/14/france-senate-muslim-veil-ban.
 Fatah, Tarek. 2019. "FATAH: Why some Canadian Muslims celebrated the Quebec hijab ban." Toronto Sun. June 18. Accessed October 2, 2019. https://torontosun.com/opinion/columnists/fatah-why-some-canadian-muslims-celebrated-the-quebec-hijab-ban.
 Cikhi, Ferid. 2019. "State secularism: veil or hijab, the real meanings and their scope." Huffington Post. March 28. Accessed October 2, 2019. https://quebec.huffingtonpost.ca/ferid-chikhi/laicite-etat-voile-hijab-veritables-significations-portees-quebec_a_23702059.
 Svihovec, Travis. 2019. "Man accused of abusing stepdaughter with broomstick over religious beliefs." The Bismark Tribune. December 6. Accessed March 30, 2020. https://bismarcktribune.com/news/local/bismarck/man-accused-of-abusing-stepdaughter-with-broomstick-over-religious-beliefs/article_4d95d50a-95c1-555f-a2bb-cca8e84dd7d1.html