Why wouldn't you communicate ahead of time that you're going to be taking a chunk of time off in the near future, specifically for something so important?
I'm not clear on when exactly he let HR know, but the original post makes it seem like he let them know a week before. I think at least a couple months notice makes more sense depending on the duration of leave.
I read that as he told HR on Tuesday, and then was fired three days later, on Friday. Not that the wife was due the following Tuesday. We don't know how far out the due date was based on what OP said.
I agree that employees should give sufficient notice for something like that. But even if they don't, that's not grounds for firing. It might be grounds for disallowing the leave until the required notice period has passed, assuming that's documented and legally allowed.
Is he supposed to let HR know when they are trying to conceive? That seems unreasonable and TMI…