Now days I don't think men always have to ask a woman out.
It sometimes depends on the circumstances and how frequently they interact with one another. For example if they're in the same classes or work together and one is aware that the other has a favorite singer or whatever in common. Either one of them might mention the event and ask if they're interested in going...etc
In fact these days a lot of men go out of their way to make it seem as if they're just suggesting "hanging out" as oppose to having a "date".
They'll casually mention something "off the cuff" thereby if they get rejected in their mind it was the activity she said no to and not (them).
Whether you're a man or a woman it takes courage to ask someone out on date. Traditionally women who asked men out were thought to be either "easy" or "emasculating". However a lot of guys welcome having the pressure taken off of them.
With regard to (why) someone says "yes" to date you'll never really know. Generally speaking men only approach women for dates whom they find (physically/sexually) attractive. There's a "romantic" interest.
They often make the mistake of "assuming" the woman said (yes) to date because the feeling is mutual. His reason for asking and her reason for going may be different!
However she may have said "yes" because he seemed nice, the play or concert sounded like something fun, she didn't have any other plans, it's a "free meal" why not? and a host of other motives.
She may have no intentions of ever getting romantically involved with him and she does not find him physically attractive. He's just nice.
Making assumptions and lack of clarity of intentions causes mishaps!