Something detestable is very bad, and it deserves to be criticised or hated. You use it for acts, ideas, and behaviour — cruelty, cheating, a cruel rule — and sometimes for a person. It is a strong, formal word about right and wrong: you are not only saying you dislike it; you are saying people should hate it. In daily talk, awful or horrible does the job. You will meet detestable more in writing and serious talk. Though actually, the -able does not mean you are able to hate it in a weak sense. It means the thing is fit to be hated.