I don't want my stuff to get used to train genAI because I think that genAI is, on the whole, a negative for society. Not because of anything inherent in the technology itself, but because of the way genAI companies are employing and marketing it. On top of that, I resent that genAI companies have abused my trust by slurping everything up to train the models without asking or even so much as a "how do you do" (this is a different than an IP law argument).
I also think that genAI companies are increasingly abusive and manipulative and don't want to support them in any way. And the fact that they often argue about how dangerous the technology is and the great risk to humanity it presents, but at the same time are eager to develop and sell it, indicates an extreme level of ethical bankruptcy.
And if you really want to prevent any chance of that happening, the only way is to take it down unfortunately.