After people do or say something that offends you, you are put off.

1. To delay; to attempt to hold at a distance
2. To turn aside; to elude; to disappoint; to frustrate.
3. To rid oneself of; take off
4. To sell or pass fraudulently

1. When you put off something or put off doing something, you delay or postpone it. When you put people off, you delay doing something they want you to do.
2. When people put you off, they do or say something that offends you.