Disclaimer- If i owned Yu-Gi-Oh it would be alot more angsty and there would be no straight people. I can't write straight people, futher more I am of the opinion that honda and otogi's fight over joey sister is not because they want to date her but because they want to date the other and are fighting so that neither dates her. Yeah I don't own it.
Joey hates seto's mutt jokes. They area a rejection to a confession he will never make. After all, he may not be the smartest person but he knows Seto hates him. Seto makes that all too clear. After all, every word Seto says to Joey says " I hate you" in the tone. Joey just hopes that his tone speaks of hate instead of pain and unrequited love.
Joey knows he is like a dog and if that were truly what Seto was saying he might take it as a compliment. Both he and Seto know other wise though, even if no one else does.
Dogs, after all are very loyal. You can hurt them for years and they'll still love you. Joey knows this better than most people. After all, Seto's been hurting him for years.