From Longman Dictionary of Contemporary Englishhave (got) something against somebody/something phrasal verbto dislike or be opposed to someone or something for a particular reasonI don’t know what it is, but Roger seems to have something against women.I can’t see what you’ve got against the idea.I have nothing against foreigners (=have no reason to dislike them). →have→ See Verb table
Examples from the Corpus
have nothing against• Now I want this distinctly understood, that I have nothing against Cleveland.• Atari and Psion, like most companies, have nothing againstenthusiasts making one or two copies for personal back-ups.• I have nothing against Mr JackNeighbours, who sadly, I understand, was killed in the war.• I have nothing against New York, I just wouldn't want to live there.• I have nothing against the Arabs ... They are the same as us.• I have nothing against the Arabs.• I have nothing against these resorts, but my own shortlist of best resorts would not include any of them.• I have nothing againstthorns and prickles so long as you can admire them from a safedistance.