Has a stranger ever frightened him that you are aware of at any point in his life? This may be the trigger. I wouldn't push him. Let him come out of his shell on his own.
At 2 years old, there is no way possible to tell what he will be like when he is older. He is just now realizing there is more to the world than Mommy, Daddy, any siblings, and himself. Given enough time, he will likely burst out of his shell and become a rambunctious little boy.
Just a little advice here, not meant as a flame or criticism of your parenting skills but let him evolve outward. Try to snip a few apron strings. I think an early school program will do well for him. It sounds like he didn't have a lot of opportunities for socialization since he was born. It could be that he feels a bit like being tossed in the lion's den so to speak.
On his first day of school, don't make a big deal. Just take him to school, give him a hug, tell him when you will be back, and leave. Don't allow him to cry or throw a temper tantrum for you to stay or him to come home. This could be one of the most rewarding experiences for him in his life up until this point. If allowed to socialize with other children, he will likely find other students who share his interests and before you know it, you will have to nearly drag him away from school by the end of the day.
I went through this with my oldest daughter. She was the quiet one; however, once I left her with her first daycare, albeit she was upset, but by the end of the day she didn't want to come home. It was like pulling teeth to explain to her that the parents of the other children were taking their kids home too so she couldn't stay there or she would be there all by herself. Kindergarten was about the same way as was 3rd grade because we moved to a new town and into a new subdivision. She had to leave all her friends behind - or she thought she did. One of her best friends moved away in 2nd grade. The first day of 3rd grade in the new school of all the kids to be sitting in her new classroom was her friend that had moved away the year before. Better still, the little girl's family lived less than a block from our house in the subdivision!
Ultimately, her friend had to move away again some years later when her mother became pregnant and she got a little brother. They had moved into these little brick apartments, the only ones in the entire town MOF because most people here own their homes and the town ordinances do not allow trailers/mobile homes, to be placed within the city limits. (It's a very affluent town albeit it's a small one; hwr, most of the residents are either doctors, pharmacists, engineers, lawyers, police, CEOs, or own their own businesses)... The apartment was entirely too small for the growing family so they found a bigger house a few towns over, which put her friend in a different school district, which both her mother and I hated because this area has the best schools in the county. It also has the highest number of students who graduate from high school to go on to college and actually complete their degrees. Our oldest graduates from college spring 2011, which is a prime example.
The kids that were here when my youngest was born were all our oldest daughter's age. There is 10 years between the girls so there was not really anyone close that my little one could play with so we enrolled her in a Mommy's Morning Out program. It allowed her to spend 4 hours three mornings a week with kids her own age. It helped her develop friendships and is probably the only thing that improved her social skills. Since I was not able to work and our oldest was working and going to school, I had time to spent with our little one. I was bed-ridden for the most part as doctors were trying to find the right medicine regimen to help reduce the pain and help me regain my mobility back after lupus (SLE) and Sjogren's were diagnosed. We spent that time with me teaching her letters and numbers using letter/number shaped refrigerator magnets then I taught her to read all before her 2nd birthday. She was even computing math problems. By the time she entered kindergarten, she was already two grade levels ahead of her classmates. There was a problem with my teaching methods that had to be sort of undone but not really. It was more of a lateral change in her learning abilities. I taught her as if she were a blind child so she was learning as a blind child despite the fact she could see. They had a teacher with the blind program come in to work with her to use her eyes to learn as well but without losing the ability to depend upon her other senses that served her so well before. Because she was academically and intellectually gifted (she was tested and put into the AIG program), and her vocabulary was so immense, it made it difficult for her to interact with other kids because they simply could not comprehend her complex thoughts and speech. Finally, the AIG teacher teamed her up with a few other AIG students from the 1st grade and things became much easier. Other kids within her grade began to excel though it would take a while for them to reach anywhere close to where she was but once they did, she began to have a little click of her own. She's extremely outgoing, busy with all sorts of programs, projects, and even the editor of the school's newspaper for two years running. This year she was even inducted into the Junior Honors Society.
You would probably not believe this but when she was around 2 to 4 years old, she would literally pace the floor at her grandmother's house as the sun began to go down and mutter continuously that she had to go home. It was time for her to go home. It was getting late and she had to get home to her mommy. It irritated my husband and I think it hurt his mother's feelings a bit but over time she snapped out of that phase too. It just took time.
So, don't judge your son by his actions especially right now. He is at a critical phase of his learning and finding himself as well as figuring out he has some independence only he doesn't know it yet. When it hits, and it will, you will wonder where that little boy of yesterday/yester-month/yester-year went... I know I do.
Nudge him out some but let him take his first steps with the exception of school because with early school programs he will have the chance to explore a whole other part of himself that he doesn't realize exists. I'm not one for pre-school or headstart programs because quite frankly, the teachers are generally unqualified to teach the children and too many parents use the program as a babysitter; however, there are not that many playgroup programs in existence. Those are the ones I'd highly recommend for younger children his age. Playgroups, which is basically what the Mommy's Morning Out program was, can work wonders for a child's self-esteem, figuring out who they are, learning they have a voice, and teaching them important social skills as well as the importance of tolerance of others who may be different or think differently.
That's just my opinion. As I said, I have a 23yo and a 13yo and so far, they have turned out pretty darn well even with all the many changes and nuances through the years and along the way from birth to now.
P.