These reasons why are Derek is mean:

He said "metal b*tch" to Cameron when she is trying to save him. Also he can't trust future John in reprogramming Cameron.

Kyle pulls out the picture of Sarah. The first words out of his mouth are "I hate that thing! That is the leader's mother...

When Kyle get missing, he rants about future John and his leadership.

Lastly, when he shot Andy, he felt no remorse, no pity and could not stop from killing Andy. As mean as a terminator.

Also does he have a secret mission to complete like Cameron (theory)?

I think he does have another mission!