When it comes to Game of Thrones, being a good father doesn't keep you alive very long. Ned Stark saw his head separated from his shoulders for following his code of honor, while any friendly fatherly peasant that's introduced is likely to get murdered by a Wildling or beaten up by The Hound for absolutely no reason.
No, it's much easier to just be a dick to your kid. Y'know, call him a 'whore' or just sentence him to death after a lengthy show trial. The usual for Westeros. Check out Game of Thrones alternative Father's Day video:
If you had to belong to any family in Game of Thrones, who'd you choose and why?
Which Game of Thrones family would you like to belong to?