Because you already have a child together I would suggest some parenting classes and couples counseling. You may be a good parent and have great intentions, but because your boyfriend is so insecure, you both need assistance.
If you didn’t have a child together, I would have suggested having a good long talk with him about his insecurities are damaging your relationship and ask him what he thinks would be helpful. If he couldn’t come up with anything and continued to be insecure, I would suggest that he is not good boyfriend material and certainly not father material. But since it’s too late for that, counseling is something that can really help, if not solve the problem.
The parenting classes can help both of you to feel more confident and competent in your actions with your child and with each other. The fact that you are willing to go with him will show that you are supporting both of your needs to do the best you can for your child. If you suggest that only he go, then you arwill make it seem like you are perfectly fine and he’s a dunce.
If you plan to stay with him and stick it out, you need a plan of action and part of that plan of action is sitting down with him, in a non-confrontational way and let him know that since you are both now parents, you both need to do more to make sure that your relationship works so that you can be loving, effective parents to your child and being insecure is going to put a damper on that, so you need to step up to the plate and offer suggestions and don’t take no for an answer. But let him offer suggestions too and try them out if they seem feasible or useful. If he is unwilling to take any steps to remedy this problem, you will have the bigger problem of raising your child as a single parent, because you won’t be able to stay with him.
Good luck, please give us an update : )