I hope you don't mind if I jump in, because I'm the female version of your boyfriend.
I am also in a deep "friendship" with someone (not sexual, my choice). I can tell he wants more, but I've reached a point in my life where I am able to "understand" my past relationships and I've also learned a great deal about myself.
If someone, especially an Aspie, tells you they aren't ready (or good -- or any other description) in a relationship, you need to hear them. That's the first issue. As an Aspie, he's going to be reviewing your friendship constantly (to himself) and the first thing he'll notice is that you don't seem to "hear" him when he speaks.
Someone who says they are not good in a relationship, and offers the example that you are too sensitive to him, is telling you the truth.
It's not necessarily saying there is anything bad with either of you, but he knows how he communicates and how others react. In fact, he witnessed a meltdown (yours) because you felt hurt. With Aspies, they are often caught in positions where people are upset with them, either because they don't understand that the words were not meant to be emotional, they were meant to be words. Also, he's seeing you have difficulty understanding him. You obviously talk about a lot of things, but it's possible he doesn't talk to you about everything, because he questions your reactions.
Personally, I don't disclose my "Aspie" label unless people need to know. I'm also asexual, which means I have no sexual attraction to any gender.
However, I *do* have Aspie traits which include often misunderstanding something in text or writing because I can't hear whether someone is being serious or joking.
While most people understand my offbeat humor, my particular friend (mentioned above) doesn't. He takes everything very seriously. I end up explaining that I was joking, or listening to very long explanations I'm not interested in -- because he thinks I truly don't understand something when, in fact, I'm being sarcastic.
He does lots of things well, and I am able to learn through watching someone else, so I enjoy those times together. We have a lot in common, a lot we don't share in common, but we enjoy each other's company and humor and do really well together.
In fact, others who see us together so often just assume we are a "couple," but I go out of my way to assure them that's not true.
Relationships mean different things to different people. While Aspies tend to be incredibly truthful, they also need to be heard when they speak.
I have had a lifetime of "other people's baggage," defining me as someone's Mother, someone's wife, someone's sister.
A relationship puts that "someone's" label back in place, and I don't want to do that. I don't trust anyone enough to be completely transparent.
I hate the idea of phone calls asking what you're doing, the idea of someone viewing or knowing passwords or seeing personal correspondence, hacking, stalking, etc.
Of course, others don't necessarily see their relationships that way, but I do. I don't want to have to apologize for someone else's behavior, I don't want to be judged by who my friends are, I don't want someone expecting me to drop everything because they say so.
So, what I'm saying, is that you might be the closest friend he has, but he's not ready to make it an official "relationship." I tend to believe these friendships last far longer (as much as a lifetime in some instances) than relationships.
I've been in plenty of dating/sexual relationships -- enough to know where I am in the whole thing. I'm comfortable having friends I feel close (and safe) with without making them an integral part of my life.
I've also seen Aspies in high-level positions who will cry and obsess if someone they don't know unfriends them on Facebook.
All Aspies are different, but the one things I've found to be true (based on experience and research) is that we don't lie.
We might not know how to express our apprehension to someone who doesn't understand, but in our hearts and heads, we know what we want.
I just tell people who want a sexual relationship that "I don't roll that way," and if I trust someone enough I'll hug or hold hands or whatever, but I'm old enough that most friends have known me a lifetime -- before my diagnosis a year ago.
All the diagnosis did was give me a reason to explain (to myself) my past history.