Re: My cat hates my new kitten
The vast majority of cats, when introduced to a new cat, will react exactly as your cat is reacting.
Most shelters, rescue agencies, vets, etc will recommends you follow an introduction process that includes separating the cats for a while, swapping scents and slowly increasing their contact with each other. Following a controlled introduction, rather than just throwing them together & forcing them to work it out, is more likely to get better results (and it won't make the resident cat(s) quite as upset). Introducing cats can take as little as a few days (rare), weeks, or even months for them to tolerate each other, and even longer to be friends.
Google "new cat introduction" for guidelines and tips.