I hear you, and I totally agree that the stewardesses handled this really poorly - they knew they were right but couldn't articulate why they were right, and it just led to confusion and frustration. I would have acted the same exact way as that guy even if I understood what they were trying to say, because what they were actually saying was stupid and made no sense.

That said, the reality of the situation is that employees of giant corporations don't have the flexibility to use their 'best discretion' (common sense) when interpreting which rules they do and do not enforce.

Or at the very least, let the dude hold his kid like they had originally offered to do and let this whole thing just go away?

This is what should have happened, and it's part of the reason why I say the stewardess handled the situation so poorly. She got frustrated and decided to just boot them off the flight instead of doing the right thing, which is letting them stay on the plane but hold the infant-in-arms, which is the context in which they boarded the plane in the first place.

I'm just super annoyed by everyone pitchforking Delta for being an evil corporation, when in reality, the policy that caused this situation is totally reasonable. It was just a perfect storm of ignorance on the passenger's part, and incompetence on the employees'.