Inyasha has dog ears because he's a dog demon. He was born from a human mother and a demon father.
A2: Inuyasha is a hanyou dog demon (half human half demon). In the manga it explains that because he is half, he is not in a fully transformed state, like his father's and Sesshomaru's true dog demon forms. So luckily, all we are left with are adorable dog ears.