Blake Roeber pens an accessible, humorous and helpful article on the subject of platonic, mixed-gender friendships. A highlight:
Platonic friendship, then, is any friendship that isn’t mediated by physical bodies. It’s friendship between Souls. It’s friendship that’s supposedly so deep that those involved aren’t even aware of (or, at least, aren’t at all concerned with) the trivial features of their respective bodies. In particular, it’s friendship where those involved aren’t at all concerned with their respective sex organs. It’s as if the friends involved are asexual.
All this isn’t to say that non-gay, non-celibate members of the opposite sex can’t be “just friends.” They surely can. It’s to say that being “just friends” takes a lot of caution. It takes care and a realistic appraisal of one’s ability to avoid temptation. It also takes the humility to admit it when one’s gotten oneself in over one’s head.
To say that Platonic friendship isn’t possible is also to recognize that, even where a guy and a girl do exercise enough caution to be “just friends,” the friendship they form will still be one between a guy and a girl, not one between two neuters.