It (kinda) takes the form “I claim there’s a china teapot orbiting the sun between the Earth and Mars. You can’t disprove it, therefore I expect you to accept that my assertion is true”.
is an analogy first coined by the philosopher Bertrand Russell (1872–1970) to illustrate that the philosophic burden of proof lies upon a person making scientifically unfalsifiable claims rather than shifting the burden of proof to others, specifically in the case of religion.
Since claims of God and lesser supernatural things often take this general form, it surprised me to hear - not too long ago - a theistically-inclined correspondent claim that you could in principle prove that said teapot does not orbit the sun as described, thus the analogy does not apply to God (so if Russell's Teapot is your go-to rejoinder to the claim that God exists, well, you’ve failed, Mister Godless Heathen).
When Russell first brought this analogy into the public consciousness c. 1952, it was in practice impossible to disprove the existence of the teapot. The technology didn’t yet exist, and certainly the will and resources to undertake such a low reward endeavor didn’t (and still don’t) exist. But wait - there’s more!
The Russell's Teapot analogy is actually too narrow in scope, given what we know about the cosmos today, if you take it literally. Which you shouldn’t. Because it’s an analogy.
Scale the analogy up to fit the cosmos that we observe today, and you could claim that there’s a pure diamond toothpick that was once owned by Lrrr, Ruler of Omicron Persei 8, that now floats freely between the Milky Way and the Andromeda Galaxy. In principle, it could be verified. In practice - extremely unlikely!
That crystallizes what I think is the point. You - Miss Straw Woman That I Constructed For This Exposition - want me to accept that God exists because I can’t prove she doesn’t. You - Miss SWTICFTE (for short) - present me with 2 equally fruitless options: believe in something that has never been verifiably observed in history, or commence my search of the cosmos to prove that it doesn't exist. That pisses me off. You're trying to get me to waste my life, and I won’t do it. There are other alternatives in life, and THAT is where I may find a fruitful path.