Welcome to the forum
I hope you have a pleasant stay
About the veil, If you ask me it comes down to this there is the pro and the contra side. I'd say the contra-hijab is divided in three parts:
1. Those who are genuinely concerned about the "liberty" of woman in Islam.
2. Those who believe that banning hijab has both benefits like better integration as well as downside like limiting religion; but feel that the later is of lesser importance.
3. And those who are contra for the sake of opposing/oppressing Islam (be that out of fear or hate or any other motive).
As for the pro-hijab I think we're pretty homogeneous.
Now obviously the angle one comes from will make that person use different arguments. For example, somebody who is genuinely concerned about the rights and freedoms of Muslim woman is then fighting a symbolic fight. Because they are not concerned about the hijab but about what they think it represents. To them we could try to explain that a piece of cloth is not an oppressive chain and we could point out the irony of trying to fight for someones rights, by taking away those persons rights to wear what they want. Since when is banning=freedom?
The second group can use several arguments from a social-psychological p.o.v. or they can also jump on the first group's bandwagon. To those social psychological arguments I'd reply that they are building on the idea that integrating into a society is more important then keeping ones religion. Obviously we disagree. Yes it's true we should try to fit in into western society, but not to the extend that we assimilate and loose our own identity and religion.
The third group will usually use any arguments available and jump on both the first and second group's bandwagon. And more then that, they will use one liners and twisted logic to defend their objective. For example, here in Belgium politicians banned the hijab in public schools under the guise of secularism and separating state with religion. they argued that there's a law that says that public schools should be neutral when it comes to religion, and hence the students shouldn't wear any symbols that refer to religion as that would un-balance the neutral image. Interesting to point out is that the very law they used to defend their ban is actually a law that was meant to protect the students in keeping their own religion. The law is meant to protect students from being forced out of their religion by school.
Well of course the matter is more complex then how I am portraiting it here. But this is what it comes down to if you ask me.