"He likes to cook with his father."
Translation:Він любить готувати зі своїм батьком.
It means 'He likes to cook with a father" not "with his father"
Relatives in English are usually "owned", but there's no such rule in Ukrainian.
Except, maybe?????, if you're from Галичина. Seriously, we always possessed our relatives in our speech. So is this a geographical thing? Or maybe a lower level of Ukrainian?
Dunno. We use both versions. If it is clearly understood that you speak about your father, you can omit pronoun