Americanism and British...

It seems to me that the conversation between American and British is going to be difficult to understand, in particular when the informalism has been used ideed. For instance, in recent days I involved in a debating about Gender, for example it is very common the usage of he or she for pets, but I argued that in British it is not correct (Formally) Tom Cat, not he cat, he dog (mistakes, please expresses your ideas.