Why is he embarrassed of me

One remark like 'my friends are a lot' means almost nothing on its own. Plenty of people hesitate to introduce someone new because they're protective of their social circle, not because they're ashamed of the person. What you're reading is the pattern across several messages, plans, and in-person moments. Look at whether he's warm when you're together, whether he asks about your life, and whether he's consistent about making time. If the warmth is there and only the visibility is missing, that's a different problem than a guy who is cool and vague across the board.

Also notice what he's ashamed of, if he's said anything. Sometimes it's a job, a living situation, a past relationship, or how he looks in photos. Those tell you what he's sensitive about, and you can name that in a neutral way without treating it as an accusation against you. If he has never said a word about why, and the distance keeps coming back, the silence itself is information.

A useful reply names a specific thing you've observed and asks a question he can answer in a sentence or two. For example, you can say you've noticed you only see him at places away from his usual area and ask whether there's a reason. That gives him a concrete thing to respond to. The reply shouldn't read like a verdict or a grievance list. It should leave room for an honest answer, including one that's a bit uncomfortable for him.

The question you ask should be one that tells you something whichever way he goes. Asking whether he's embarrassed of you invites a reflexive denial. Asking what would make it feel easier to meet people from his life gives him a chance to explain and gives you information about whether he's working on it. Keep the message short enough that he can reply without drafting a speech, and avoid stacking several topics into one text.

Send the message once, in daylight, when you're not already annoyed from a long day. If he answers warmly and proposes something concrete, you have a real signal to act on. If he gives a vague reply, let it be vague and see what he does over the next week. Don't send a second message explaining the first one. A follow-up that clarifies your point is fine once. A follow-up that repeats the question with more force usually pushes him further back.

If days go by with no reply, or he deflects again, you have your answer for now. Stop investing extra effort into the question and let his behavior speak. You can still keep things light and enjoyable, but don't keep building a case for why he should show up. Decide what you need to see before you'd stay, and stop when he's shown you he's not going to provide it.