Indicates negative emotions, like dislike or resentment, towards someone or something. She seems to have something against the new policy.
Pro Tip 2/3
Without Evidence
Sometimes used when there's no clear reason for the negative feelings. He doesn't know why, but he has something against that place.
Pro Tip 3/3
Personal Issues
May suggest personal issues with someone rather than professional or factual disagreements. I have nothing against her personally, but her work needs improvement.