As Birmingham Metropolitan College, one of Britain's largest institutes of higher education, bans Muslim women from wearing veils on the grounds of "security risk" – then changes its mind within days – we ask: what, precisely, were they imagining?

Was it a sort of Mr Toad scenario, where a villain creeps about disguised as a woman? Or that Muslim girls themselves would tuck Berettas under their veils, ready to whip out if a teacher prescribed too much geography homework?

I suppose either is possible and the former has, I think, actually happened once or twice in human history – but this offers only an opportunity to quote, as so often in these paranoid days of ID checks and CCTV cameras, the old Ben Franklin line: "He who values security above liberty deserves neither."

The problem, though, is that there are two potential threats to liberty in this scenario, which clash with each other. Bear with me; I feel one of my epiphanies coming on. I'll just take my pills, and then I'll be with you…

OK. Let me start by saying that I know very few Muslim women who veil their faces. The Muslim women I know well dress the same way I do (although they wear jeans, which I never would because I'd look like one of the Moomins.)

The only veiled women I've met are casino wives who sit quietly behind their husbands during play, and all I've really thought is: "So she has to wear the full niqab but you're allowed to gamble, eh?"

This is the nub of what I am going to call, because I've always secretly wanted to be a mathematician, the "Birmingham Liberty Paradox".

Forbidding the veil is an infringement of liberty. But so, it would seem, is wearing it. What should the well-meaning white liberal think? (Hurray! The editor of the Observer gives £5 to anyone who manages to work that question into a column. If you can legitimately make it "the well-meaning black liberal", you get £10.)

Whatever veiled women say about modesty, tradition or feeling closer to God, we in the £5-aspirant group worry that they are oppressed: that it is about being hidden and silenced.

Naturally, one wants students to integrate and mingle. Half the point of education is to build peer groups and social bonds. To the uninitiated, a veiled face inspires shyness; one is less likely to start a conversation, nervous of everything from intruding on privacy to failing to recognise that person if you meet them again. (Lord knows I forget people's names when I've seen them naked, never mind fully veiled).

But these were not the grounds on which Birmingham Metropolitan College rolled out their ban. The talk of "security risk" itself hardly sounded like a friendly hug across the cultural divide. They have now altered the rule to say that veils will be allowed, but hoodies won't – presumably hoping that those who put their religion as "Jedi" didn't really mean it.

Still, one worries that veiling the face inhibits free social action and that it is intended to. Many of us feel despondent that it applies to women only, and fear that it is supposed to make them invisible.

Here comes the epiphany, and I apologise for bringing it down to my personal concerns – but I have to believe I'm not the only one in this boat. It's about my name.

I had an instinct to take my husband's name when I got married. It felt like a romantic statement of pride, love and permanence, and of doing what's always been done in my family.

But I was scared that it might be mistaken for a blow against feminism. Scared that it might be a blow against feminism, or at least disrespectful of it. And nervous that, without the label I'd soldiered under for nigh on 40 years, I might feel like I had disappeared. ("Mitchell" is a pretty inconspicuous surname anyway; I'm fond of my curious birth name that people mispronounce and spell as "Cohen" one email in three.)

Please don't suggest that my husband could change his. If a fashion is new enough to be remarkable, then it's not for him; he'd be as comfortable re-launching under his wife's name as he would getting a Harry Styles haircut and twerking in London's hottest nightclub.

I chose, complicatedly but honestly, to use a range of names for a while: mine, his (ours), and sometimes both at once in the American tradition. I decided to try the long version in the Observer this week, with the feminist defence that a married woman changing her name is, like giving up her job to raise children, oppressive when it's obligatory, but confident and happy as a choice.

And then it hit me, perhaps more slowly than it's already hit you: that's what women say about the veil, isn't it? That it's a strong and happy choice; that their grandmothers (or young cousins in Saudi Arabia) might not have had that choice, but they do in Britain today and they make it in glad and grateful acknowledgement that it isn't mandatory. Of course, bystanders murmur that they simply don't realise how deeply they are in the grip of the patriarchy that devised the system. Just like some people might say about me.

And maybe they're right! Maybe I just think I'm enjoying the freedom to choose my own name, when I'm actually brainwashed by an antiquated patriarchal idea from which others have rightly sprung away.

But I know this much: I will never again think that a veiled woman is strange or unknowable. Whether we're both right or both wrong, I will recognise her as very familiar – only, perhaps, having made her choices more decisively than I make mine. And you only need to see someone's eyes to know if they're smiling back.

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