Is this even rude?

[SquarePeggyLeggy]

I think it’s very rude to respond to the question: “how are you?” With: “very busy”.
To me, I feel immediately shut down, like the person doesn’t want to be troubled with my contact and questions, or that they’re far more important than me because I have the time to ask after them. Aren’t we all busy? Busy is not an emotion, or a state of health, which is what the questions asks?
I’m coming off the back of having relatives visit for Christmas dinner (allowed where I live) after I’ve spent two days cooking and preparing, 40 minutes late, working on phones while I served up, and answering this to the dinner chat before leaving abruptly at the end. I was busy too! Cooking and cleaning for you sods. Is your busyness more important than mine?

Quote not quite

In itself, I don’t think it’s rude to respond and say you are/have been really busy. This situation seems a bit off. Generally however, sometimes people are SO busy they don’t get a second to even ask themselves how they are doing...it’s just running from one thing to the other, especially at Christmas time when you can be juggling lots of balls and desperately trying to keep everything going. I find that most people know and understand that responding about how busy things have been is not rude.

If you invite them in future you could say "Would you like to come for xmas dinner or have you got too much on?" Hopefully you'll get next year off from hosting anyway.