I think it is great that you are accessing resources for your family.
If you are not feeling up to par for homeschooling-- and I want to say that there is nothing wrong with questioning your abilities, my sister home schools her three boys and it is pretty much her 40 hours plus a week job-- please consider trying to ride this out before removing him from school. I know he's upset about it, but sometimes, kids can get themselves really stressed out before something and then realize later on that they enjoyed it. (I know this can happen for us, even as adults)
One thing I would consider is, whenever possible, not mentioning the upsetting parts of school or focusing only on the negatives. When he comes home, I'd ask very specific things like "who did you play with today at recess?" or "What did you choose for sharing time? Who did you do that with?" Avoid questions that ask him to judge or assess school ("How was school today?" "Did you have a good time at school today?")... these sort of questions allow a great entry point for "bad" "no" and other negatives. It's okay if he says "I really felt bad when..." and then you might even take it to the next step "wow, that does sound like a hard moment for you. What do you think you could do next time X happens?" Help him to work out or visualize positive solutions to those small problems.
Last year, D., my little guy was in kindergarten and he really struggled socially. I heard lots of "no one wants to be my friend/no one played with me"... when I investigated further, gently, I discovered that my son was so insistent on playing certain 'stories' (superheroes, robots, super kitties, etc) that kids would say "well, we're playing such and such" other activity and he'd just decide that since they didn't want to play what he did, they weren't his friends. I did have to make it pretty clear to him that playing with other kids meant that you took turns with your friend when choosing the activity-- you couldn't have it ONLY your way all the time. Most of the year, he had this complaint and it was so hard to see/hear him struggling in this way.
In first grade, however, this has changed. He's gained maturity, learned how to find friends to play with, learned to be more flexible and to go along with the group. The point of my telling you all this is simply this: kindergarten IS hard for some kids. It's SO much easier, socially, to be in preschool or at home. In preschool, teachers are more likely to be advocating socially for each kid and helping them settle problems through social coaching. At home, there is very little challenge socially. But at school, this is huge!
The other reason I would encourage you to stick with it is that pulling him out now may seem like the easy, obvious solution, but he needs something to go *toward*, otherwise, it will later appear to be a no-confidence vote on the part of the adults. Maybe the counselor will suggest a well-accredited charter school with a smaller classroom size, or could help your family develop some strategies for positive verbalization. Last year, the counselor at our school suggested some very helpful strategies; one boy, he was afraid of-- instead of talking about the fear, I changed my own language :"I am really looking forward the time when you can enjoy being around Johnny." D., this can change so much-- before the school year was over, my son was asking for playdates with this (not really scary) kid.
Keep us posted-- I am sending you thoughts of encouragement. It WILL get better (and then the kids always come up with something else for us to worry about!) ! :)
ETA: I really liked what Angela S stated about her experience with Homeschooling. I'm not trying to diminish his fears, but dealing with the social anxiety piece of this is really so important, and it sounds like changing situations may not really relieve this entirely.