My 2¢: a bully is trying to intimidate, a father is not 'intimidated' by his own child.
Here's my attempt to not do a mouth-breathing bully-dad:
Try imagining the same scene but with a nurturing father who wants to guide the son to arrive at some moral or personal growth, working through the problem, and bonding. The father wants the boy to come to him with problems, until he is mature enough to stand on his own – that's the goal.
Now turn that character upside-down –– it is a lecture that goes nowhere, words to provoke not think, unreasonable ultimatums, punishments that are completely unrelated, 'should have known better', no faith the boy can grow or learn from mistakes, and no filter on his own emotions. There is no logical way the son could appease the father because the father doesn't understand the goal.
No need to explain it. In real life there are a scary amount of people who seem to be 'faking it' without understanding the goal. Maybe he had a dysfunctional father himself, or maybe he just never wanted kids and there is no upside for him. I would expect other signals of selfishness/lack of empathy from this character (a room where the son is not allowed, marital affairs, resentment, avoiding).
If the character sticks around, he will need to be more than just contrarian or he will start to feel like a prop.
A flawed father might leave room for some sympathy, or at least character depth if the father should be seen as a realistic person (not an abstractly 'pure' antagonist).
The father might always center himself (narcissism, insecurity) without any consideration how the boy got in trouble in the first place.
The father might project his own desires/fears onto the boy, using him as a proxy for everything the father isn't able to be, or has sacrificed for.
Family dysfunction might transfer blame, or otherwise use the weakest family member as a scapegoat, with other family members participating in the pattern usually to avoid it pointing at themselves.
A family trauma might have the father in a perpetual grief-coping loop where day-to-day problems are never resolved because the father can't break from the thing that keeps him moving forward. Extra pressure to not disrupt the father's career/ personal time/ church activities – something that has taken the place of spending time with his family.
Lastly the father might just be overwhelmed, or have a personality type that is too analytical/impersonal, and the end result is the boy's problems don't amount to anything important. The father would feel impatience and frustration that the son can't just 'keep it together', meanwhile not offering any useful advice or constructive empathy.
I think a common denominator of a flawed father is some behind-the-scenes character building where he has erased the son and replaced him with an idea which the son doesn't fit. Whereas Anti-father is negative parenting, the Flawed Father is in a relationship with the son that is not based in reality.
In both cases the dad is failing to perform basic functions as a father, failing to correctly address the problem, and failing to see what his son needs. Have an idea what's going on behind that character and then let him reveal his truth through what he says. He will ultimately steer the conversation to what he believes.
The son is powerless to change the dynamic but is forced to be present. He knows this doesn't lead anywhere, and he has to perform convincingly before the father will stop.
As author you are teasing the father's true nature while putting unfair agony on the sympathetic son. That power imbalance is important, it is why the father can be unreasonable. Whatever the details it will feel abusive.