The terrible point is, basically, "men and women just can't help being sexually attracted to each other", and it permeates the entire article. Even when the author is attempting to question this basic premise it still warps his phrasing. Why is it terrible? Well, because it's not true, for one. But beyond that, it's a remarkably heteronormative idea; it comes coupled with an inherent mental model that everyone is heterosexual.
Consider: Is a male homosexual who hangs out with the other guys on his team going to be unavoidably attracted to every single one? If he hangs out with the girls on his team are they going to be unavoidably attracted to him? Does any homosexual individual, thus, unavoidably cause unrequited feelings of lust, no matter whom he hangs out with? Will a bisexual individual be unavoidably attracted to every person he meets? It it, say, just a feature of gay life that they are constantly frustrated as they keep meeting straight guys whom they can't help but be attracted to (whereas straight males can just avoid hanging out with females and remain unfrustrated)?
No. That's not how it works, for anyone, gay or straight. Apart from a few relatively rare mis-fires, we are only sexually attracted to people who are attracted to us. (This one of of the major misconceptions that led to restrictions on homosexuals serving in the military. And there's no question it's a misconception.) Most pairs of people - regardless of gender and orientation - simply don't have that sexual spark.
The good point hidden in the article is that American culture has no real idea of "friendship" in a sense that people from other cultures either now or historically would recognize as such. American's just don't have friends. We have weak acquaintencnes. Why? Nobody seems to know. But it's something that probably deserves more attention.
But in this context, the question "can men and women be friends", in the context of American culture, actually has an answer. "No". But since the same answer is true of "can men be friends" and "can women be friends", this doesn't mean quite what it seems. :)