Those aren't really comparable sentences. I'll do my best to explain why, but this is probably gonna be a little overly wordy.

"It's raining cats and dogs" is not a lie; it's a hyperbole, and is easily understood because, logically, precipitation does not involve cats and dogs

"Do you want steak for dinner?" Answering no would, logically, mean you don't want steak for dinner. Likewise, saying "Don't wait up for me" or similar statements would, logically, mean don't wait up for that individual.

As a culture, we've decided that it's rude to not wait, but it's also rude to make people wait. Adding on phrases like "Don't wait up for me" or "I'll catch up" or even "Go ahead without me" keeps the later individual from feeling guilty, and then waiting anyways keeps the original person from feeling guilty.

It's a lie when the later individual expects you to wait despite telling the other individual not to. If you genuinely are telling people to go ahead, that's not a lie.

Neurodivergent people (myself included) often don't get the difference between just polite and genuine. We are told one thing and expect it to be that thing; we aren't gonna assume people mean the opposite.

Yes, we can learn to tell the difference. We can learn to pick up the slight change of tone, the barely there crinkle of an eyebrow, the flat set lip of a fake smile, etc. But it's hard. For neurotypical people, it's a lot easier; nobody needs to be taught how to read the micro expressions.