Man of Honour
They let men do the approaching because that is considered the norm, it's also the easier position to be in as you don't have to be the one getting rejected. I happen to lurk a lot of different threads in these forums and I can tell you more than a few people have been discouraged from internet dating because of constant rejections, it's not easy putting yourself out there and getting shot down again and again. I'd like to think that any guy who got hit on by a female would probably consider it a refreshing change, but I like that you're trying to assert exactly the opposite.
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I agree with you in general, especially when it comes to the extreme antimale sexism in domestic violence and the oft-repeated lies about how men consider it normal and acceptable to beat and rape women, but I think you're missing something regarding this particular issue.
Someone approaching you for sex/a relationship is flattering and a refreshing change...when it's a change. When it happens all the bloody time, it's an annoyance even when it's not done badly (which it often is, especially when alcohol is involved as it often is).