Java users have to use double dispatch and such, because Java only implements dynamic dispatch on the type-erased type of the first function argument.
The last bit of the GP comment is an example of the sort of thing that isn't possible with generics in Java, because the PetTrainer-of-Dogs and PetTrainer-of-Cats are indistinguishable at runtime. If you want to solve the problem with dynamic dispatch on the type-erased type of the first argument only, you could *stop using generics*, write a separate class for each generic instantiation you would have had, send every pet to every trainer, and have each trainer check the runtime type of their argument and do nothing if it's the wrong type. This probably isn't what anyone really wants to write or an acceptably cheap thing to do at runtime.
Nobody actually deals with PetTrainers but people do deal with MessageSubscribers that work more or less exactly as described, and the type system does nothing to help. For a concrete example of the horrors of double dispatch, you could see the wonderful book Crafting Interpreters.
The last bit of the GP comment is an example of the sort of thing that isn't possible with generics in Java, because the PetTrainer-of-Dogs and PetTrainer-of-Cats are indistinguishable at runtime. If you want to solve the problem with dynamic dispatch on the type-erased type of the first argument only, you could *stop using generics*, write a separate class for each generic instantiation you would have had, send every pet to every trainer, and have each trainer check the runtime type of their argument and do nothing if it's the wrong type. This probably isn't what anyone really wants to write or an acceptably cheap thing to do at runtime.
Nobody actually deals with PetTrainers but people do deal with MessageSubscribers that work more or less exactly as described, and the type system does nothing to help. For a concrete example of the horrors of double dispatch, you could see the wonderful book Crafting Interpreters.