It makes sense. He's a narcissistic manwhore who has indirectly caused the deaths of thousands of people by allowing his technology fall into the hands of terrorists, and he tends to be a class-a jerk and yet he's still probably my favorite Avenger. You can't hate him. It's weird.
The Captain America: Civil War trailer is actually an elaborate Yo Momma joke told by the Winter Soldier. (Given the likely cause of Maria Stark's death, Bucky probably shouldn't try anything similar with Iron Man.)