Fiction loves a good bad dad. Not a father with nuance, but a father that inadvertently makes their child's life miserable by giving them a very specific plot purpose, whether that be literal (he's been kidnapped!) or psychological (he's never going to approve of you!). These dads love their children, but they're also terrible people.
And we've laid them all out here! Be aware that these are fathers who ruin things in more subtle ways than being outrightly physically and verbally abusive. These dads don't specifically mean to be horrible -- but that doesn't make things easier on their poor kids.
The Dead Dad
The best unintentional awful father is the dead father. Why? Because a dead father isn't a character at all, he's a plot device. He'll leave his child an inheritance regardless of the burden it may put on them. Or an unfinished great work for them to complete. Or a nemesis. Yeah, dead dads always seem to have people who hate them who carry that hate against the child, too.
If it's just the dad who's dead, then the unlucky surviving mother will get a lot of "this wouldn't happen if dad were around." If it's both parents who are dead, the character is likely to only care about the fate of one of them. (Caring about both parents is too hard, I guess.)
The dead dad doesn't mean to ruin their kid's life, but they still manage to take it over, even though they're not there. It's so easy to excuse anything a character needs to have for plot purposes by saying "dead dad did it" that it happens way too much.
The most egregious example in my mind is actually the horrible Jem and the Holograms movie, where the titular character and her sister live with her aunt because their father died. Oh, what about their mum? No clue. Also, he left something behind for Jem (...just Jem, not Jem and her sister) and Jem is obsessed with it. He hits pretty much every one of these tropes.
The Criminally Unaware Dad
If you've got a story where a kid is having amazing adventures and the dad's not dead or criminally busy, then the only explanation for the kid getting away with things is that the father just. Doesn't. Notice.
It's always frustrating because these dads are portrayed as generally awesome, but the fact that they have managed to miss that their kid is fighting demons or wandering around in a spandex suit does make you question how competent they are. Because I remember being a kid and I got nothing past my parents. Nothing. And I get that maybe I was a bad liar, but still: how are any if these kids still hiding things from the people they live with?
The Comedy Dad
If I could eliminate one comedy trope from the hands of bad writers, it would be the comedy dad. The dad who tells embarrassing stories, the dad who tries to be "with it" by using "hip" lingo, the dad who shows up at school to yell "Just picked up your medication for this private condition!" Once in a while, sure, a dad will not realise he's embarrassing his kid. But the dad who does literally nothing else? Don't even have the character then.
I'm looking at you, parents from the Transformers movies.
The Workaholic Dad
Or, you can be excused the things you don't notice by simply not being around. They don't mean to hurt their kids, they just have things to do. And, in some cases, what they have to do is work really hard to provide for their child. Or they're the ones working on something that will save the human race. Or, you know, they're a supervillain. Supervillains love their kids, too. (And I nominate Norman Osborn as the patron saint of the bad dad.)
The absolute sign you're dealing with one of these? If the child asks them to be there for just this one thing -- graduation, wedding, performance -- and they don't make it. Or, they show up, but leave halfway through with a mobile phone to the ear. They may as well leave behind a sign that says "everything is more important than you, son!"
On the scale of unintentionally bad dads, the workaholic is right in the middle in awfulness. There is no reason they shouldn't know that they're hurting their child, but they're not actively trying to turn out emotionally stunted and/or needy kids.
The "Follow in My Footsteps" Dad
Hey! Want to absolutely make your kid crazy while thinking you're securing their legacy? Well, then spending every waking moment talking about how they have to do well in school, marry the right person, stay away from scandal, and just generally be perfect in exactly the same way that dad was. Because dad has picked a successor, regardless of the child's actual temperament or skills.
Again, they want what's best for the family, so they're kind of blind to the fact that this is hilariously awful parenting. Bonus points if the dad's settled on the oldest/male-est child, even though they have another kid that actually wants the job. Another set of bonus points if the father pits the kids against each other to determine who is most worthy. (Go watch The Lion in Winter or Empire, for that matter.)
The Never-Pleased Dad
The "Follow in My Footsteps" Dad can very easily mutate into the Never-Pleased Dad. This trope is beloved by comics. These dads are perpetually disappointed in their kids, even if their kids are practically killing themselves trying to make them happy. Batman does this to every child under his care. Norman Osborn picks this one up, too. Odin is also a shockingly awful father. Still, kids who try desperately to a dad who refuses to acknowledge their accomplishments do tend to get a lot done.
The Forbidding Dad
Again, this a father who wants what's best for a child but has a very specific view of what that is. Don't waste your time on music, please enjoy this maths problem instead. Stop reading fantasy books and get to work. No singing, only basketball!
Look, just letting a kid do whatever all they want all the time is bad, yeah, but this dad exists solely for the purpose of being eventually proven wrong. He's a walking lesson, not a dad.
The Overprotective Dad
Just let the girl do things, arsehole. My god.