"What harm is it to you to shove a free test up your nose for ten seconds to ensure you don't pass the virus on without knowing to someone who might get seriously ill."
Is it really free though? The cost of having to isolate is quite high. (Mental health, lost income, inconvenience, stress, etc.)
If you all test and get to all meet, good for you all.
But what if you all test, and some don't get to meet?
It's a bit of a blow to those that can't. But good for you that you can still meet.
And consider those that can meet. Seems you're all Covid-free —good for you. But will you stay Covid free? (Not likely —it's endemic. For some in some jobs, even to escape it for a few weeks would be a surprise.)
So you're really saying that you don't want to knowingly catch it from family, but still accepting the fairly high chance of catching it in future anyway from randoms in shops, kids at school, work, and so on.
That's morally quite a questionable position in my opinion.
Would it be more honest to simply say that you don't want to meet your extended family? ;-)