>>52603487Paradox Pokemon have been recently discovered in the context of SV and your character is one of very few people to actually capture them.
You can extrapolate in-universe reasons for why they can't breed, why they don't have genders and why they don't evolve by Pokemon terminology.
Pokemon that are in the No Eggs Undiscovered egg group are there not necessarily because they can't breed, but rather the methods for these Pokemon to breed haven't been discovered/documented by humans in the Pokemon world. That is why the egg group is referred to as No Eggs Undiscovered: Their Eggs haven't been discovered and documented by Pokemon research.
As to why these Pokemon don't have genders: Once again, these Pokemon have been recently discovered and captured/documented by your player character, so the methods are still unknown.
Pokemon with no gender are generally considered "Gender Unknown" meaning they don't necessarily have no gender, but it's literally unknown to modern Pokemon research. Nobody can fucking tell.
Basically, nobody fucking understands or knows these creatures well enough.