To him, this whole deal has become far more trouble than it was worth (although to be fair, it paid a considerable fortune, and would've solved the crisis at hand with Jabba). First, it was obvious sooner than he would've liked that his passengers were on the run from the Empire (which he he has already reminded himself a dozen times as being the reason for the crisis with Jabba). Second, their simple trip to Alderaan instead landed them within the heart of the Empire's new weapon, which is so massive he at first mistook it for a small moon. Third, the princess annoys him a great deal.
Don't get Han Solo wrong. He loves a good woman, but the princess was never what he had in mind. All the trouble this deal has already caused him counts for nothing as soon as she enters the equation. She makes a bad situation worse in an instant. For all his years smuggling, he never thought it could be that easy.
They've just escaped a deathtrap, which she created. The princess is distracted by the farmboy who is now the sole-remaining member of the passengers he took aboard, besides the old man who would've given the princess a run for her money if they had ever met. It's all he can do to avoid rolling his eyes constantly during the whole ordeal.
Now he has a moment to think. If they can even get off this space station, he's got to decide how much he'll help them. He can do that, and then leave them far behind, which is an okay thought (will certainly help him bring the necessary funds to Jabba), or he can cut his losses. Which is to say, get rid of the princess.
He opts for the latter. He and Chewie spend some time running away from Stormtroopers, which presumably the princess and the farmboy are doing elsewhere. There's no time to talk. He doesn't concern himself with what his buddy will think about it anyway, not in this instance. Besides, Chewie's clearly no friend of hers, either.
Incredibly, they manage to survive the next few minutes, and have found themselves back at the hangar bay where the Millennium Falcon awaits. He sees the princess at a distance. His fingers twitch on the Imperial blaster he's liberated along the way.
Hey! As far as he's concerned, she feels the same way about him, right? And the way things are going, will anyone even notice what happened? It's either her or him.
Han shoots first.