It's not weird to spin something that might have been positive into looking funny in the light in a rap battle bruh lol what aren't you getting about this.
And If I'm battling cardi I'm using all types of shit like why make a family and pose like you happy with a nigga that has a new baby every 3 weeks. It's an exaggeration, but I can do what I want with the narrative when the context clues are already there.
The point is to make us question drake's integrity when, up to this point, we've all seen him as a pretty good guy and savvy businessman. How are you smart when you knock up a porn star? How good of a dude are you when you deny your kid then turn around use him as a publicity stunt. It's even more etherous that push beat him to punch and has control of the narrative when the eventual reveal does happen.
And for the record I don't disagree that drake can't do a rollout for his kid. He can do what he wants. But for the purposes of a battle, it's your job to consider the audience and sway public opinion in your favor. Push is doing that by challenging his whole persona.