The reason cats can't be vegan is that they cannot produce an amino acid called taurine, which is something dogs and humans can produce (but which we also get sometimes from dietary sources).

Most dietary sources of taurine are meat. This is why dogs and humans "can be vegan" but cats "can't". However, vegan taurine is made and can be bought as a supplement, both for humans (if you want to ensure you get some taurine in your diet), but also in properly made vegan cat food.

It seems to me then that cats can be vegan, just not without intentional effort to ensure proper supplementation of taurine. That is, they couldn't be vegan in the wild (where the only source of taurine is meat) and you can't just start to feed them a vegan diet without taurine and expect the cat to be healthy and survive.

In fact, cats fed a proper vegan diet tend to have better health:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10499249/

I think the question is really what you are feeding your "vegan" cat: if you have managed to find (or make) a properly fortified vegan cat food it is theoretically possible to feed your cat a vegan diet.

This all feels a bit like the "controversy" around feeding young children and babies a vegan diet: done poorly it can be catastrophic (pun not intended), but it's entirely possible to have a healthy vegan diet when enough effort is put into ensuring nutritional needs are actually satisfied.

That said, I also know of two other vegan responses:

1. for some vegans, having pets is not vegan to begin with, so a "vegan cat" is a contradiction in terms even if you fed them a vegan diet, you still wouldn't be an ethical vegan by owning a cat. This is admittedly a less commonly held view which centers ethical veganism on the rights of animals to have autonomy, which if plausible in some ways seems at least impractical in the case of domesticated animals. There are questions of the harm that might be caused by choosing to treat cats not as pets but as autonomy-rights-bearing "wild" animals, but those ethical vegans might rightly point out this doesn't undo the cat's rights and the practical questions should be handled separately.
2. most vegans I know IRL just feed cats a non-vegan diet, acknowledging it is safer and more reasonable for their cat than trying to figure out a way to feed them a vegan diet. Good vegan cat food isn't that common or easy to find as far as I know, and I assume it would be outrageously expensive.