Why does it upset me when people "play the Jesus card"?

I’m not religious. Sometimes, in debates with Christians, they state their position and then add “That’s what Jesus told us.”

It annoys me, but I can’t quite grasp why. It gets on my nerves even when I agree with the other party’s position. Why?

For what it’s worth, I try not to seem annoyed. Also, I don’t want this thread to turn into a flame war. I’m just interested in exploring my mind.