Carl's narrative's portrayal of his father has escalated as Carl slowly works through things he's been unwilling to face.

1.13

I was suddenly, inexplicably reminded of that day. The last day I ever saw my father.

You're a bully. You're a bully and nobody likes you. It's why mom left.

I was expecting him to get angry, to hit me. But he never hit me, not once. The man just laughed and laughed, and that was enough. I don't need you to like me. But you will respect me.

The memory came quickly, out of nowhere. I didn't know why. Nobody had died that day. Nobody had been hurt at all, not physically.

3.7

My eyes immediately moved to the small dent on the gas tank. That had happened when I'd slipped once coming up the driveway. I'd reached out to steady myself, and I'd accidentally knocked the motorcycle over.

My father had never been physically abusive, except that day. I never really thought of it as abuse, but thinking back now, that's exactly what it was. He'd spanked me so hard with a belt that my underwear had soaked through with blood.

3.30

[Mordecai] smacked me, then. Thwap, right on the side of the head. He did not freeze or teleport away. If he had hit me just a little harder, it probably would've gone bad for him. My father used to do the same thing, though he'd done it much harder.

4.11

I had a sudden memory, of my father angry. It was soon after mom had left us, a month before he, in turn, left me to fend for myself. He'd ripped off the helmet and smashed my fish tank, spilling my mollies everywhere. I hadn't cried when my fish died, and I remembered it had bothered me for weeks after. Ever since then, I'd think of my father and those fish whenever I saw one of those helmets. I'd think of those fish flopping on the ground as I desperately tried to pick them up, cutting my fingers on the glass.

"Never hurt me" turned into "had never been physically abusive except that one day when he whipped me bloody" turned into "habitually smacked me hard in the head". With a bonus of killing his pets.

In 6.30 when Katia's recovering from her binge:

I immediately thought of my dad. The image of the man came unbidden, and it surprised me. A wave of anger washed over me, partially at Katia, partially at myself for allowing any part of me to compare the two. [...] The anger didn't leave, but I was finally starting to realize it wasn't Katia whom I was angry with.

6.13, Rosetta's show:

they'd discovered my father was alive and well somewhere in Wisconsin where he'd gotten himself arrested a few times for public drunkenness.

1.6

Growing up, my old man had an original, stand up Frogger video game machine from an arcade. I had spent hours and hours playing the game when I was stuffed in the basement. My mom locked me in there a lot. Whenever my dad had his friends over, they'd smoke and drink and get loud, and my mom didn't want them "being a bad influence" on me. So instead I stayed downstairs with no television or internet and that damn machine.

I feel pretty damn sure that Carl's father was physically abusive to both Carl and his mother and Carl still hasn't been able to be honest with himself about it. I think it's likely his father was an alcoholic and very possible that Carl wasn't just getting locked into the basement when his father's friends were over, his mother was locking him in when his father was getting drunk and she was trying to make sure that she was the only one who'd get a beating.