The "advice" is often to lie. "Tell them you're busy and can't do it" Etc
See I don't think there's anything wrong with saying this. Or in lying, to an extent, if that's what you need to do to to get an unreasonable person to back off.
But saying you're busy/not available is fine, if you don't want to do something, then it's a perfectly OK thing to say. With some pushy people, if you give a reason, they will argue with your reason or try to offer a solution. Eg you can't do something because you have the kids, oh it's OK X will have your kids, or oh it's OK you can bring them. When you don't want those solutions and they are not helpful. I have learned that just being unavailable, not free on that day etc sends a clearer message.
A friend of a friend who has a senior arts management job told me that when she first started her career she thought making herself constantly available and adaptable, and being willing to help out and take on extra work, was a good idea. She did, was run ragged, no one appreciated her and she never got recognised or promoted. She was annoyed and decided to start saying no more often. She would say she wasn't available for things (not everything, but within reason) because she had an appointment or a meeting. She didn't explain or say what appointment or meeting, she just said that. She said to me "it doesn't matter if it's a hair appointment, or a "meeting" with yourself for a quiet coffee. You don't need to say what it is."
She immediately got way more respect, got treated as way more important, got rapidly promoted and ended up at the top. Now of course she also needed to be good at her job for that, and she is, but the point is having no boundaries and never saying no just made people disrespect her, offload shit onto her and made her a target for the worst type of lazy user, and made people see her as a pushover. I think this is especially important for women who are socialised to try to be helpful and kind, and can end up running everything - often very competently - because they don't want to say no, for very little reward.