Can almost hear Carly saying, “Give me your hand, give me your hand, give me your damn hand!!”
Exactly right - she was trying to raise his hand. He's the presidential candidate, so his hand gets held up by hers. But the oaf couldn't figure out that to be dominant, he had to let her lift his hand. He also couldn't figure out how bad an unbelievable amount of finger wrangling would look on camera.
Cruz is just wound too tight, he didn't understand and he fought her over it. It's ridiculous. She probably yelled "what the hell is wrong with you" later at him.