I'm going to call this logical fallacy the '50 Shades of Grey' technique. It's where you argue that the overwhelming majority of cases is invalidated by the mere existence of outliers.
"Overwhelming majority"? Care to back that up with statistics? Oh wait, you can't because you're speaking out of your ass. Besides, the point several of you are trying to make is not "The majority of men can't be friends with the majority of women", it's "men and women can't be friends". Even if cases where men and women were friends were in the minority, the blanket statement is invalidated. If this were any other topic you guys wouldn't put up with wild and ridiculous generalizations in order to support a point for a second!
If you want you can fool around by putting down as many asterisks as you like:
Men and women can't be friends*
* unless the parties are not attracted to each other
* unless both parties are married
* unless the guy isn't a "real man"
* unless the female is "using" the male as an "emotional tampon"
* unless they're technically just "acquaintances" by some arbitrary definition
* unless they're friends, but not "platonic" friends according to the dictionary
* unless the guy is holding out hope that they'll fuck
* unless they are forced to spend time together (ie: they're co-workers)
Note that in all these cases, the man and woman involved are happy to call each other friends and don't give a shit about your "rules". If two people consider themselves friends, who are you to tell them they're not?
When you have to keep "qualifying" what you mean in order for your statement to work, eventually your original statement just doesn't hold any sway any more.
If you accept that some men can be friends with some women (and your statement implies that you do), then the statement "men and women can't be friends" is false.
Don't get me wrong, I'm happy to continue this discussion indefinitely, but you're going to have to come up with some better material.