Connie,

This guy’s behavior sounds like he has an avoidant attachment style. “Avoidants get easily overloaded with too much intimacy and need to regain their space and autonomy by moving away. When their partner gets too close, or stay close for too long, avoidants start to pull away.”

Look it up in learning more about it and how to deal with it.

How long did you know him before he asked you to be his girlfriend?  How many times did you meet?