It’s important to support your partner and show them that you are on their side when someone is being unfair to them, but in a healthy relationship, you also need to give them a reality check and speak your mind if you don’t really agree with their point of view.
Their gym installed a new route and it meant that many people didn’t do well, including the OP and her boyfriend, as it needs time and training. However, one of the women there seemed to glide through and her only mistake was that she didn’t hold for 5 seconds when finishing the route, as it is the proper way.
The boyfriend took offense and didn’t talk with his girlfriend for the rest of the night, and when they were going home, he finally said that he felt betrayed when the person who was supposed to watch his back was on the side of the person who publicly humiliated him.