The two definitely have a sort of love-hate relationship. Inuyasha loves to pick on Shippo and hits him a lot and Shippo in return loves to poke fun at him, but their fighting is almost brotherly and Shippo does look up to Inuyasha as an older brother. Inuyasha isn't one to show his feelings so it can come across that he doesn't like the kid, but he often has tiny moments of affection that show he does care. For example, in episode 72 (Totosai's Rigid Training), when fighting for the tiny Banzo and his father, he's asked why he was doing so and said it was because Banzo reminded him of one of his friends (meaning Shippo). Also in episode 21 of TFA, Inuyasha has a rather serious moment and tells Shippo he can't come with them to fight Naraku because he will have to look after the village if they don't return then in some versions refers to him as "Great demon Shippo." There are many more little moments that reveal Inuyasha's soft spot for Shippo despite their quarreling nature.