It has nothing to do with their organs. It has to do with past experience. All of the men I've met, besides my fiance, have been total douchebags and just after sex all of the time. My entire family cheats on one another constantly, and all of my old friends from school share that same attitude. From personal experience on my side, the majority of women aren't looking for a male friend to play video games with. They're looking for a compatible figure, regardless the other person's relationship status.
Meanwhile, my fiance's experience with other males and females alike have been 95% negative. He has few friends he would deem friend-worthy, since the rest are morons and interchange partners like no tomorrow.
From our experience, women and men alike are primarily just after sex when they befriend someone of the opposite gender. The wrong idea might even rub off without you knowing, and that's not good.
As said, it works for my relationship just dandy. Why not avoid trouble before trouble starts? I realize that there are women and men who aren't like the 95% we've met in life so far, or have shared experiences with in friendship. Unfortunately, the 5% don't come along too often. I have one or two female friends in real life, and that's better than 20 idiot friends really. Same with him. I'm friends with his male friends, and he's friends with my female friends. We're friends with all of our co-workers, regardless gender as well.
Just do whatever works for you, really. This works for us, and it's not a restriction. We feel it's how a relationship should work and we have barely any issues at all. My fiance and I are alike in almost every aspect, including food, games, morals, and values. I'm happy that I found someone who's so alike to me :< We've been together for nearly three years now with just a few misunderstandings here and there. We tried the "anyone can be a friend" idea at the beginning of our relationship for about a year, and it didn't work too well, because of the intentions of the other person. This sprouted jealousy and anger towards the "friend" and pretty much an argument with either me or him, too, depending on whose friend it is. It didn't work for us because of the intentions of others, and we've just decided it's best to avoid all of that altogether and befriend only the same gender, co-workers of any gender, and friends of each other of any gender.
It works for us. If it doesn't work for you, then so be it, but we have our reasons for rejecting other-gender friends, and those reasons are legit.