Why the issue of the Islamic veil? It rests at the center of the clash between Islam and the West.
The veil seems to be used to keep the "wrong" men -- those who are not close male relatives or guardians -- at a distance. Relations between the sexes, apparently, must be controlled, the more rigorously the better. There is also the assumption that women are worth less than men [Qur'an 4:3; 4:34; 4:11]. They inherit less; they often cannot travel, even to see a doctor or pick up their children at school, without the permission of a male relative or guardian, and they may be beaten or divorced without recourse. They are subject to a different set of the laws: men may, under certain circumstances, marry up to four women -- not only as if they are men's property, but property that contains one's honor in a way that, say, one's chair does not.
Muslim women wearing the niqab full-face veil. (Image source: Darrell J. Rohl/Flickr)
Men and women are kept segregated. It appears concluded that if a man and woman are left alone in a room together, there might be passionate sexual activity at some alarming point. Marriage laws are also restrictive; this alone is a blow to our hopes for social integration.
Western societies, in contrast, make it possible for us to choose. In freedom to choose: to be conformist or non-conformist, to wear the clothes we prefer or read the books we select. Western democracies have come a long way since my early student days in Dublin, when a literature student could not buy novels such as Lolita, The Catcher in the Rye or Lady Chatterley's Lover. We take for granted freedoms that many people living in Muslim states today can only dream of, or behold goggle-eyed from afar.
What kind of moral imperatives have led to the insistence that women cover their faces, or considering an interest in wine or chess or even cricket as mortal sins deserving punishment? This austerity is not unique to Islam; it has parallels in many religions. In Islam, much originates in social custom rather than in the Qur'an or the Hadith literature [deeds and sayings of Mohammad]. Although the hijab does not appear in the Qur'an, which tellingly insists only on women's chests being covered [Qur'an 24:31], the headscarf has now become a symbol of a woman's identity as a Muslim. Many of these rules and regulations, however, have moved to the West and have created conflict where none was before.
Some Muslims, it seems, refuse to integrate for reasons of religion, through the communal doctrine of al-wala' wa'l-bara -- fear of losing one's attachment to one's primary community. Other Muslims might refuse to integrate from the fear of challenges that life in the West entail, such as deciding whom to date or marry, what books to read, what religion to believe in or not believe in -- things we do every day and probably do not even think about.
Al-wala' wa'l-bara' has often been translated as "loyalty and enmity," although it is more nuanced than that. Wala' means something like "friendship" or "benevolence," as well as "fidelity." Bara' should be bara'a, meaning "being free" or "disavowal" or "withdrawal." The idea is that Muslims should stick close to those who are near, to their friends -- who should be only Muslims --- and to everything associated with Islam. And that they should withdraw from, and consider themselves free of, non-Muslims. As the Qur'an (Surat al-Ma'ida, 5:51) puts it:
O you who believe! do not take the Jews and the Christians for friends; they are friends of each other; and whoever amongst you takes them for a friend, then surely he is one of them; surely Allah does not guide the unjust people.
Muslims apparently also consider themselves free from our books, our art, our democracy (made by man rather than by Allah), our open debates — in short, our civilization, which is probably perceived as tempting, but impure, dissolute -- with its promise of torment in hellfire mentioned frequently in the Qur'an. 
A list of what is disapproved of in relations with non-believers, from the book al-Wala' wa'l-Bara' by Shaykh Muhammad Saeed al-Qahtani, includes:
CHAPTER SEVEN: TYPES OF ALLIANCE WITH NON-MUSLIMS
Twenty Forms of Alliance with the Disbelievers
1. Contentment with the disbelievers
2. Reliance on the disbelievers
3. Agreement with Points of Disbelief
4. Seeking the affection of the disbelievers
5. Inclining towards the disbelievers
6. Flattery of the Disbeliever's faith
7. Taking of Disbelievers as Friends
8. Obedience to the Disbelievers
9. To Sit with Disbelievers who Ridicule the Qur'an
10. To Give the Disbelievers Authority over Muslims
11. Trusting the Disbelievers
12. To Express Pleasure with the Actions of the Disbelievers
13. To Draw Near to the Disbelievers
14. To Aid the Disbelievers in Wrongdoing
15. To Seek the Advice of Disbelievers
16. To Honour the Disbelievers
17. To Live amongst the Disbelievers
18. To Collude with the Disbelievers
19. To Revile the Muslims and Love the Disbelievers
20. To Support the Ideologies of the Disbelievers
Taken together, these tenets indicate that, for Muslims who take their religion seriously, there can be no question of integration at any level.
The rejection of Western values by strict Muslims, as opposed, say, to the Amish, is that it has often been accompanied by extremist opinions and actions. The Amish do not say they plan to bring down Western society or to impose their will on non-Amish. Extreme Muslims do.
Although political correctness will tell us to accept everything other cultures do, there comes a time -- not just for Westerners but for Western Muslims, too -- when, if there is no evaluation of what is accepted, our societies risk becoming hollowed out from within.
Not all Muslims, of course, follow all prescribed doctrines; but divisions, though perhaps inevitable, are not helpful in any society, as I know too well from an upbringing in Northern Ireland.
Women, supposedly "protected" by shari'a law, seem especially harmed. Schoolgirls in Saudi Arabia on March 19, 2002, for example, pushed back into a burning building by the "morality police" because their hair was not covered and they were not wearing black cloaks, found themselves protected to death.
Women in Islam -- often with no say free of intimidation or repercussions -- are often subject to practices such as domestic violence, unequal justice under shari'a law, stoning, lack of freedom of movement, and (the totally un-Islamic but tribal) honor killings and female genital mutilation. A Muslim woman who is raped needs to produce four witnesses to the crime to testify that she actually was raped -- an impossible standard of proof -- or the rapist can be freed on the grounds of having been falsely accused. The man is never to blame: if he was driven to rape, it can be seen as the fault of the woman who allured him.
Everyone, further, is harmed by an atmosphere of aloofness and secrecy. Many Muslims, perhaps to make their faith appear benign in Western eyes, will often understandably speak or write in a way that portrays their religion in the best light -- a practice that can involve keeping the less-benign passages of the Qur'an and Hadith from public view. The ultimate practitioner of this approach is Tariq Ramadan, grandson of Muslim Brotherhood founder Hassan al-Banna. The much-lionized Ramadan persuades half the intellectuals of France that he is an honest broker who could not possibly support the views of the Muslim Brotherhood, despite, among other matters, his unwillingness to condemn execution as a punishment for adultery.
As for the aloofness, in the same way that one sees Palestinians and Jews working together at Sodastream in the West Bank, it would be heartening to see even more Muslims not only working with non-Muslims, but taking part in social activities, playing cricket with non-Muslims on Sundays as some Muslims in Yorkshire do, engaging with the local chess club, and other such pastimes. In a few generations, Muslims might even feel British or American or French, in addition to retaining their faith, the way Jews, Italians, Irish or Polish Catholics do in the United States. It is therefore all the more disturbing to read in the British Policy Exchange survey of 2007 that the young Muslims of the newer generation are often even more conservative and highly radicalized than their parents and grandparents.
If integration is the goal, something appears to be going remarkably wrong.
 While a Muslim man can marry a non-Muslim if she converts, a woman may only marry a Muslim man. A non-Muslim man cannot marry a Muslim woman unless he converts to Islam. In May 2014, a 26-year-old woman doctor, Meriam Ibrahim, eight months pregnant, was sentenced to death for having married a Christian man. Although the sentence is said to have been revoked, it is not at all clear that it will stay revoked.
 "But those who disbelieve and deny Our signs -- those are the companions of Hellfire." Quran 5:10. See also: Quran 74:26-7; 64:9; 54:47; 2:119; 7:41; 79:36; 22:51; 29:55; 33:8; 37:69-73; 46:31; 88:2-7. "And whoever desires a religion other than Islam," says the Qur'an, "it shall not be accepted from him, and in the hereafter he shall be one of the losers." (3:85).
 See Paul Berman, in a penetrating study, The Flight of the Intellectuals, and the French journalist Caroline Fourest in Frère Tariq.
 Polish Catholics in the US are beautifully portrayed in Keith Maillard's perceptive and moving novel, The Clarinet Polka.