2) Albus can't stand being thought of as his father's clone.
At the train station, when he left for his first year at Hogwarts, Albus was terrified of being sorted into Slytherin.
Once he boarded the train, his opinion changed. He and Rose ended up in a cabin with three other first years. The very first thing they all asked was "what's it like being Harry Potter's son?"
Albus' answer of "it's like being anybody else's son, really" did not go over well.
Hagrid the half-giant was still on first-year duty, and Albus had the misfortune to make it ahead of all the other first years to where Hagrid was standing with his lantern.
"Ye look jus' like yer ol' dad did at yer age," Hagrid told him with a clap on the shoulder that nearly knocked Albus off his feet (and off the train platform). Albus smiled weakly and squeaked out "oh, really? I had no idea." After all, it wasn't like he'd heard that his entire life or anything, from everybody who knew his dad as a kid and a great deal of people who didn't.
He somehow managed to get shoved to the front of the pack of first years once they arrived at the castle, and was met with the venerable Professor Flitwick, who smiled hugely at him and said, "Ah, another Harry Potter! A chip off the old block, no doubt what house you'll be in!"
That was when Albus made the decision to ask the Sorting hat to place him somewhere, anywhere, but Gryffindor.
James looked downright stunned when the Hat placed him in Slytherin.
Rose hugged him on her way to take her place at Ravenclaw, and whispered, "A right chip off the old block now? You show them, Al!"
Albus could hardly suppress his manic grin for the rest of the night.
Well, most of the night. When he reached the Slytherin first year dorms, one of the other boys asked, "So how will the great Harry Potter react to his son being a Slytherin?"
Albus, without really even thinking about it, snapped back, "I'm not my father, and I can be in whatever house I choose!"
The boy grinned broadly, and held out his hand. "I'm Scorpius Malfoy and I'm not my dad either. Want to be my friend?"
Albus, after staring at the outstretched hand and its blond-haired, blue-eyed owner for a moment and trying to figure out if the boy was off his rocker, took his hand and shook it. It couldn't hurt to have a loony friend. After all, Albus' entire family was crazy. Scorpius would fit right in.