"il gatto" is an article and a noun. "di lui" is a preposition and a pronoun. And, Italian pronouns nearly always have a preposition with them. They just do. They don't like being "naked". In English the pronouns often stand alone.
Just my basic understanding. I am open to correction.
Because saying "I go towards to him" is both improper English and redundant because in this instance "towards" and "to" describe the same action. So essentially you are using two adverbs (towards and to) to describe the verb "go". Plus, It's also implied that when you say "I go towards him" that you are "going to him". I don't know the specific linguistical reason but this is my best guess for you. Perhaps someone smarter than I could elaborate more for you