While it is a cute thing to say and I can appreciate the affection for the animal...legally, it is not your son no matter how many times you insist that it is. It is a domesticated
pet.
But do find it strange when folks use their doggie as a substitute for a child. My opinion--but it is weird to dress out your doggie and treat it like a baby and I cannot believe how much that industry makes.
I have cats--love them to pieces, but my cat would not have it if I insisted on putting on a cute outfit.

And yes--i do baby talk them. But I also realize they are not my daughters and son--even when I did not have children.