To disavow something is to say, often in public, that you will not own it: you are not responsible, you did not know, or you want no part in it. A company might disavow a fake message sent in its name. A politician might disavow a helper’s rude comment. It is a formal, slightly legal-sounding word. In everyday talk people more often say “I had nothing to do with that” or “that was not me.” Disavow is what you use when the break needs to be clear and official. Though actually, it is not the same as disagree. Disagree is “I think that is wrong.” Disavow is “that is not mine.”