Is a guy who acts like this insecure?

He does sound insecure, and yes it would be good to ask him why. Maybe he was bullied as a teen or he has had bad experiences with girlfriends in the past and has made him insecure. However if he thinks you are looking at another guy you should make it clear that you are on a date with him and not with the other guys. If he is getting like this on a date just imagine if this guy were your boyfriend?