The one true answer is that that's how Game Freak wanted it to be. Anything beyond that is speculation, unfortunately.
But, speculation is fun! Look at the list of Pokémon that learn Dazzling Gleam. Most of them have some way of either emitting/refracting light naturally, or using their psychic powers to do so. Whereas if you look at Azumarill, nothing about it screams "glimmering lights." It's an egg with ears and a tail. So, thematically, it having Dazzling Gleam doesn't make much sense.
Of course, not all Pokémon that learn Dazzling Gleam necessarily fit with the theme (like Chansey), but I think what I listed above is a pretty solid theory as to why Azumarill does not have Dazzling Gleam, despite being a Fairy type.
I hope this helped!