When something threatens you (or at least is perceived to threaten you), your brain gives you anger as a response. Every emotion has a purpose, and the purpose of anger is to prepare you for conflict. Your brain is expecting you to settle the issue. "Something bad is happening to me, and I'm going to beat it."

Depression turns this around: "Something bad is happening to me, and I can't do anything about it." You don't feel anger, but instead you resign yourself and fall into despair. The fact that you're feeling angry at all is great - it means some part of you wants you to put up a fight.

"Irrational" anger is really displaced anger. Something bad happened to you in the past, and but it wasn't safe to do anything about it. Feelings are just conscious awareness of your emotions, and they dissipate over time, but emotions are a whole-body thing, not just limited to your conscious awareness. The transgression is remembered and stored up.

Now something happens that resembles or even the slightly resembles the past transgression. When the minor thing happens, your brain sees it as "round 2" (or even round 3 or round 50 if it was an ongoing thing), but this time you can do something about it. The angry emotions from the previous transgressions and the current transgression are all felt at once, and targeted at the current transgression. This time you're really going to annihilate whatever's hurting you.

This might make more sense from an evolutionary point of view: if your family were speared by wild boars when you were a kid, when you mature into a full-bodied adult, all of that accumulated anger is useful. Every boar in the forest is going to feel your wrath, protecting your family. The amount of anger in the present is proportionate the the threat and hurt built up in the past. It's to your advantage that the more damaging the threat, the more aggressively you should attack it (the more anger you should feel). Anger is a protective thing.