Why is it that anything a guy or girl enjoys doing that seems to be for the opposite gender qualifies them for this trope? So what if a guy likes cooking or is interested in fashion? Or if a girl enjoys rough sports or hates dressing "girlish"? Why does that have to mean they could be gay?
Because society still enjoys thinking of actions or preferences as gender-specific, and also tends to think of a gay individual as more akin to a member of the opposite gender. Yeah, it's dumb.
As said, it's related to gender roles. Society is very strict on what "Boys should be like" and what "Girls should be like". Anyone who doesn't fit the roles completely are accused of being gay or transgendered.
What do you mean, "accused"?
there's not really a better word for it, at least not that I can think of.
How about "assumed to be"?
Actually "accused" is closer to what someone who cares so much about gender roles would think.