I'm not sure if you're odd, buckets :) but - yeah, lots of women do expect that.
There are quite a few posts on MN about whether a woman should offer to go Dutch on a first date, and consensus is hugely split. Some women say they'll be offended if the man accepts, some women say they'll be offended if the man doesn't accept. Some women say it's wrong to even offer to go Dutch.
Not one woman, that I saw, said that she would offer to pay for the man too, up front. All would either pay half, or not at all.
And lots of posts about waiting for a man to ask for the first date too.
It's not an equal world. If men sat around waiting to be asked out, then very few people would go out on dates.
If a woman suggests it first (and often it's phrased as 'so are you going to ask me out or not?') then it's refreshing. But refusal often offends. Sometimes I'm not yet interested enough in a woman to go and meet them, as I can have a banal conversation with lots of people. If I'm going to probably be expected to travel somewhere, and pay for someone's drinks, they've got to be interesting enough to deserve that. I'll generally do the asking.
But then I think it can also be 'put up or shut up' as some people just like to chat endlessly - especially the married ones.
If a guy doesn't message you first, he may just not have seen your profile. Or he may have, but he was alread talking to someone else. Or he may have thought you were out of his league, or he may not have fancied your profile particularly, but any port in a storm, or.. or..
You can't tell.
I've only ever been messaged three or four times by women whose profile I actually fancied. Almost all the time it's by someone I wouldn't look twice at. Almost all my first dates come out of me messaging someone I liked.