I mean, boys and girls can be friends without there being anything between them, right?
It's not easy. You'd have to look past gender, but you've already categorized. I mean, does it matter whether your friends are boys and girls? Even if you're one to value diversity, shouldn't diversity of thought be more important?
For most, there's bound to be some innate form of physical attraction when they're friends with the opposite gender. For reference, check this video out.
I haven't read through all of your posts, but I had related problem in trying to befriend a girl this past term. We were floormates (she moved out of the building for unrelated reasons), and we had a course together. Large class of around 140 people. One day, a few weeks into the term, she randomly decided to sit next to me, even though we had barely talked to each other before that. Afterwards, it became a common thing. I started sitting around the same area, and she'd somehow recognize me and take the seat next to me if it were open. This girl is pretty attractive, so I actually wanted to make a move. But I was also afraid that, successful or not, it'd ruin our "friendship."
But anyway, back to your question: Do you think you'd want to befriend a girl that you didn't hold some physical attraction towards? And even if by some spontaneous event, you were to form a friendship with that kind of girl (perhaps by common interests), wouldn't you eventually become attracted to her? I can't say these are fully rhetorical questions though. Maybe you think differently than I do. But based on that video, that seems to be the way a good deal of men think. It's harsh, but I consider most of the girls I've associated with as either acquaintances or people I wanna hook up with. Occasionally, a girl comes along who I actually want to make a relationship out of, but those are rare. The people whom I hang out with most are guys, and I think that will always hold true (besides girlfriend/wife).