Get Someone's Back Up Meaning

(idiomatic) To annoy or anger a person, either deliberately or inadvertently.

Example:   That joke really got my boss's back up.
1970, James N. Casavis, Principal's Guidelines for Action in Parent Conferences, ISBN 9780137020010, p. 121:
  Telling someone that her child can and should be doing better and not offering some solutions immediately gets my back up.