Sometimes asexuals will say, "We talk too much about what we don't do and what we don't experience. What about what we do experience?" I agree, and you could consider this a response.
But first, check out this diagram, which has been spotted in the asexosphere:
It's supposed to describe attraction, and it makes my head hurt. But something on it really gave me pause, and that is "platonic attraction". I experience no sexual attraction, very little romantic attraction, and I rarely go, "Wow, s/he is cute!" (which I think some people consider "aesthetic attraction".) But I realized that what the web of mystery calls "platonic attraction" is a whole 'nother story. In the web, my platonic attraction would probably be rated somewhere around "high" whereas everything else would be low or nonexistent. I have a high "friendship drive", if such a thing even exists. I know that after sex drives and romance drives, another long drive seems excessive. But this is the thing I do experience, and I venture the same is true for many other aces. There also must be non-asexual people who experience more platonic attraction than either romantic or sexual attraction.
(And let's pause for a minute to acknowledge that "attraction" is so tied up with something sexual that it sounds vaguely creepy to be attracted to friends in any way, even if it's entirely nonsexual. But moving on...)
For me, I was in my mid-20's before I realized that no, I could not be everyone's best buddy if I only put in enough effort and was flawless in all my social interactions. I actually didn't know that some people will always be casual friends or acquaintances, and will never become your best friends, for whatever reason. I can attribute part of this to a lack of social knowledge. But maybe the other part comes from a desire that things would be otherwise. I don't just desire human companionship, but very close friendships. I would be happy to have a "partner"-type relationship that was with a friend, for instance.
Especially in the years before I learned I was asexual, I always wanted a boyfriend. However, I did zero work to make this happen. On the other hand, I was very committed to friendship, and had no problem putting in the hours it took. Surely, that means something. While I wanted a boyfriend, I could live without him. But I knew I'd be miserable without friends.
The issues one may face experiencing high platonic attraction in our society are various. But the main one is that I often feel I can't tell my friends how important they are to me, because they might consider it weird or out of place. Maybe I just suck at expressing my feelings, but I'm pretty sure that can't be all of it. Often I shy away from even writing about friendship here, because I know some of my friends read this blog. I don't want them to think, "Well, she says friendship is important to her, but that's not clear from her actions!" Maybe my feelings and actions aren't always aligned very well. But anyway, this is getting slightly embarrassing, so I'll be moving on again...
Anyway, I'm realizing that platonic attraction is one more reason why I don't like the romantic/aromantic binary. For aromantic and barely-romantic people who still want friends, wouldn't a more accurate name be "platonic asexuals"?