In general I agree with the premise that men and women can't be friends, but I also understand that there are exceptions to every rule. I'd like to throw out one that has held true for me.
It always starts with attraction for the guy, so at some point I've been interested in the girl(s) in question. But it is either rebuffed or can't happen for various reasons (already has a boyfriend/husband, coworker, EQ-based long-distance e-lust, etc.). At some point, over considerable length of time, I have come to realize that I dodged a bullet and I would never, ever want to be in a relationship with any of these women. Being friends is fine though because I honestly have zero interest in them anymore. Now, it is also true that they almost universally offer me next to nothing in the way of friendship because they are women that I don't want to fuck, but since I'm putting nothing into the friendship really, I'm not losing anything either.
One of them did call me out on treating her differently than I used to (EQ girl), and I bluntly told her that was because I wanted to bang her before. She got pretty offended by it at first, but being female she literally has almost no friends and I was fine with never calling her again, so she got over it.
I'm sure some armchair psychologist will say that I still want to bang them, that's why I keep them as friends, but I can promise you that's the furthest from the truth. If you know a girl long enough without getting to bang her, you eventually find out what type of person she is anyway; I would have simply found out quicker if I dated her, but might have overlooked some of it too if the sex was great. In this particular case she's gone from mysterious hot chick in EQ I knew almost nothing about to a decent looking chick that embodies almost everything I despise: vegetarian (but hypocritical of course, she'll eat chicken or fish...but only if it doesn't look like it came from a live animal, so no drumsticks for example), returned baby shower gifts that weren't on the approved "toxin free" list, refused to eat any bread out of the basket because I had taken one roll out before using her hand sanitizer, won't eat at a bbq unless she watches the cook use different utensils to cook her food so it doesn't get any of the beef/pork/whatever on it, breastfed her first kid until he was at least 3, I stopped asking after that because she had her second kid, AND she used to love to fucking play alts over mains constantly! The insanity! I could go on and on. I actually tell her that I feel sorry for her husband all the time because he has to put up with her insanity.
I don't care how hot a girl is, if she's that opposite of everything I believe in, I'd have buried her in the backyard long ago if I had let myself get trapped into that life.
So yeah, men and women can be friends once the man realizes he really doesn't want the woman anymore. We won't be sorry if we never hear from them of course, but we can still be friends.