It's very easy to find the wearing of the veil offensive.
What it says to me is that the wearer sees me, a man, as being so untrustworthy, that I'm not even allowed to look at her face. I find that offensive.
It also says to me that wearer is someone who is unwilling to assimilate into the society in which they choose to live. I find that offensive.
It also says to me that the wearer thinks so little of the society that surrounds her, she is willing to cut herself off from the rest of us. I find that offensive.
I don't particularly like any public demonstration of any religious beliefs. The difference is, I'm willing to tollerate it, because not everyone does or has to think the same way as I do.
Why the hell shouldn't the wearing of the veil be seen as offensive?