Coming from an airline background the whole things sounds strange to me, I always let new FO's fly unless things were particularly hairy and even then I could select which legs I flew and which legs they flew. If the guys in the training department said they were qualified and they got through OE that's good enough for me; I didn't expect perfection from someone brand new and I was more than willing to help them if they needed it but I wanted them to fly and get experience so if something happened to me the passenegers would get to the ground in one piece. Different culture I guess; a CA who doesn't want the FO to fly is probably insecure and a somewhat uptight, weak pilot anyway. There are so many former airline guys at NJ that I'm surprised this sort of thing happens.
On the other hand, if I had to start over at a place like NJ I wouldn't take it personally. If you have substantial CA experience then you know what it's like to fly a plane and you know how to do it. If the other guy wants to do all the flying so be it, it doesn't hurt my ego and the paycheck still gets cashed either way. My advice would be to go to work, do your job well, and when the job is done go home, cash the check and forget about it. If the company wants to pay you to read checkilists and talk on the radio who cares? Be sure to remember to say "excellent landing Sir (or Mam)" and just let it go; life's too short to worry about stuff like this.