CBS shot down Jeff’s original idea— which is why they showed Reid being attracted to JJ. I never got that he was asexual, although a lot of people seem to want to see him that way. He has shown that he is attracted to women, but that he has trust issues as well as self esteem issues. He’s been misled in the past and humiliated by girls, so he is a bit afraid to open himself up to further ridicule. He’s been shown checking women out.
He was clearly interested in Lila, but he was conflicted because he didn’t want to violate the rules and he didn’t want to deceive her. He had a hard time believing that she legitimately liked him and that it wasn’t because she was in a stressful situation and trying to seek comfort. Obviously that relationship didn’t pan out.
I think that once Reid was able to push aside his anxieties and fears, he was actually interested in a sexual relationship with Maeve. He wanted to marry her and have children with her. Unfortunately the writers couldn’t picture him in a real physical relationship like that so they took a page from the women in refrigerators protocol.
I know a lot of fans want to keep seeing Reid as an innocent virgin, but I wish they would give him a legitimate love interest where he gets to explore physical intimacy (we don’t need to see it, mind you) and cohabitation. Unfortunately I don’t think the writers can imagine Reid like that and I don’t trust the current batch to pull it off in a believable manner.