It’s not the emotions that are petty. It’s how he controls them – what he says and does with those emotions.
Anger isn’t “bad.” Weaseling, unfairly demanding, seeking revenge, obsessing on not getting one’s way, pushiness, shouting, whininess, etc. are inappropriate reactions to anger in a situation like this one. (I’m not accusing the OP of demonstrating any particular behavior.)
And petty is such a good word to describe these behaviors.
The store made a mistake by promising to hold an item without getting any contact info to the person they were holding it for. If they did they could have called him and inquired why he still hasn’t picked it up. At the very least they should have agreed upon a timeframe. As it stands they made the right decision by honoring their end of the bargain. It would be really unfair to the person they were holding it for if they went ahead and sold it anyway because they thought he was taking too long.