How old is too old to be a parent?

I recently saw a photo of 80 year old Robert De Niro with his new baby.

Unsurprisingly, many comments said "80 is way too old to father a child."

Surprisingly, a LOT of comments said "My dad was X years old when I was born, and I hated it. He wasn't able to throw a ball with me like normal dads, he was always the old dad, and he'll die way before I'm ready."

If you hear the age of expecting parents, at what age do you start assuming the kid will feel that way?

(Context: I'm old, my husband is older, and I'm pregnant. I want to know what we've gotten ourselves and our future kid into.)