We all know that Sherlock is mentally ill. He has self-esteem so low his soul-blood is hypo-tonic. He has clinical Depression up the wazoo. He's an addict to a life-threatening degree. He's a dick-and-a-half to everyone, including his BFF 5-ever, John. The man is damn loony.
However, if he's not actually Asexual, but heterosexual, then he is even more vulnerable.
First, I'll go over the reasons why the BBC version of Sherlock is probably straight rather than Ace. Then we can talk about how his illness is reflected in his sexuality.
S3E3: When Magnusson evaluates Sherlock thru his mental catalog, he puts "normal" under the category "Porn Preference". If "Normal" means "Average", then it probably means average for a man. In most studied countries, 90-96% of people claim heterosexuality, so the average porn preference for a man would probably feature women.
TAB: In Sherlock's mind, his bestie John confronts him about his secret affection for Irene Adler, and questions Sherlock embarrassingly on his "need to be alone". John claims he doesn't believe Sherlock honestly isn't attracted to women and romance. Obviously, this all takes place in Sherlock's brain, so Sherlock is questioning himself on these things.
Later, in the crypt with the secret society, Sherlock is explaining the "League of Furies" to John when he says "A league of furies awakened. The women I...We have lied to, betrayed." Sherlock is manifestly guilty about how he's treated women in his life (specifically Molly and Janine). He's guilty enough to dream about it while trying to solve a crime. Problem is, he's screwed over a lot of people in his life (Mycroft, John, Lestrade, his parents etc.), but why is he so concerned about the girls who loved him?
S2E1: Moriarty begins Sherlock's Fall by sending Adler to him. I'd like to think that Moriarty is particularly adept at reading Sherlock, and people's wants and needs in general (it's how he makes his living, much like Adler). However, what is the point in sending an overtly sexual women to an Asexual man? Moriarty knew Sherly never had relationships, nick-naming him "The Virgin". Why not send a purely intellectual foe? Why send a woman at all? Especially, why a dominatrix? She didn't win. Moriarty wasn't completely correct in his assessment of Sherlock's weaknesses. But she got really, really close.
Adler: Brainy is the new sexy.
The eternally articulate Sherlock: ajldmflmg
So, if Sherlock is straight, what would all this imply?
Well, for one, that he's afraid of sex.
Mycroft taught him to abjure emotion ("crack in the lens"). In his mind, emotion would ruin the only thing Sherlock has to hold on to: his intellect. Sherlock is a graduate Chemist (S3E2). He knows that chemically, sex involves emotion (dopamine, oxytocin). Therefore, he avoids sex, and by extension, women. This is what Moriarty caught on to, and why he not only sent an intelligent woman to play Sherlock, but one who would have no problem making advances on him. Yet, Adler and Moriarty knew that Sherly Temple wasn't just going to fall for anyone who stripped in front of him. They needed to involve both his intellect (all the puzzles) and his emotions ("Damsel in distress...are you really so obvious? Because this was textbook") simultaneously. Had Sherlock been more honest with himself about feelings, he probably wouldn't have let her get so far. But his self-esteem is so low, he couldn't figure out the pass-code for her phone. Until the last minute, he couldn't figure out that a women could have really fallen for him.
His horrible self-esteem is also why he didn't realize that Molly was actually into him, and not simply susceptible to flattery. It's why he couldn't deduce at Christmas that she'd dressed up for him, or that the present at the top of the pile was for him.
He thinks himself unlovable ("I never expected to be anybody's best friend"). He's constantly suspicious of people, that once they get to know the real Sherlock, they'll leave. That's why he had little problem tricking Janine. He knew it wouldn't work out anyway. She only liked him because he put on a different face.
He's slowly unlearning this mindset. John has spent every season proving Sherlock wrong about himself.
I think some of this stuff will prove to be the final problem in the final season.