Being in a relationship with someone who is extremely jealous, is incredibly difficult. You need to decide if his emotional needs are going to fit in with your lifestyle. It might just be that the two of you just have to very different ideas about relationships and his views might be too conservative for your more modern mindset.

I do think it is really great that he admits you are doing nothing wrong and that this issue is something he needs to deal with, but what is he doing to deal with it? Sulking for an entire day because you spent time with a friend is very extreme.

If he wants to get comfortable with dating someone who is outgoing and has lots of friends, he will really need to work on himself. In the meantime, be brutally honest with him about how his extreme jealousy is making you feel. He needs to know that it is a real problem for you. If he thinks you are just a bit annoyed, he won't change. He needs to know that this is literally driving you crazy. My suggestion would be to go back to him, let him know how much this bothers you, and then talk it out. Is there anything that would help him be more comfortable with your friends? Maybe if he got to know your friends a little better that would help? Or maybe if he spent more time with you and your friends and could see that you interact with them the same way you interact with your female friends and that nothing weird is going on? But other than that, he really needs to figure out how to curb his jealousy on his own. You are doing nothing wrong here and if he does not get his issues under control, he is just going to push you away.