Dean is terrible at apologizing. He just can't do it. And when he does? He can't even look into your eyes while doing it.

Hell, he deserved loads of apologies, especially from his dad, who was most of the time out hunting, leaving Dean with Sam alone, being just little kids. Making Dean grow up too fast and be afraid of the dark knowing that actually something could appear and hurt him and his brother.

After your fight, he felt bad. You yelled at him, but still, it was for a good reason. He literally made himself a bait to the fucking spirits─ almost getting himself killed.

He thinks he can make you forgive him with his shitty apologies and his puppy eyes (which he absolutely can), standing in front of your motel room. Sam was the one who made him do this. Told him he was being a jerk by simply not talking to you after the fight and he should apologize, properly.

"Brought your favorite... poison, or whatever." he murmured, and by 'poison' he meant iced coffee, he doesn't know how and why do you like this thing. "Can i come in or are you gonna yell at me again?" he tried to joke, even though he could barely look you in the eye.

He brought iced coffee because he knows you like it, as a form of apologizing. Maybe later he'll use his words... maybe not.