Get/put somebody’s back up
Definition 1 of 1
Pro Tip 1/3British Roots
Originally British English, it's used in various English-speaking countries, understanding may vary. 
She's English, so saying something cheeky might put her back up.
Pro Tip 2/3Emotional Response
The phrase often describes a defensive or indignant reaction, rather than just annoyance. 
When accused unjustly, that's likely to get his back up.
Pro Tip 3/3Social Context
It's used in informal conversation and may be inappropriate in formal or professional settings. 
At family dinners, avoid topics that could get people's backs up.