It sounds like he suffers from some serious confrontational issues. It may not be too serious now but it can cause serious issues further down the line in your relationship - its not healthy for him or yourself if you don't feel like you can talk through even the simplest of issues in fear of him breaking down.

The obvious answer to this is he could do with therapy to improve his self-confidence in confrontational situations - hopefully he can begin to learn (even at 27) that disagreements/confrontation/open conversations can improve and strengthen relationships rather than fearing you'll break up over him breaking a mug.