When you look on a pokemon's page, you can see all of the egg moves that they can learn. Suppose you choose to teach your new pokemon one, and go to the page of that move. Before you would be a list of all the pokemon that can learn that move. When figuring out how to get an egg move for a pokemon, it would be really helpful to add the pokemon that can learn the move's egg group(s) under it on the move page to hlep match up the egg group of the pokemon you want to breed the egg move onto and a pokemon who can learn the move of a compatible egg group. After all, in the whole sea of pokemon that can learn a specific move, there may only be one that is in the same egg group as the one you want to breed. Adding a 'show egg group'/'hide egg group' button on the move pages would be really convinient to find a compatilble pokemon rather than following all of the links to check the egg groups.