Okay, Alfred's jacket only works to calm Alex down when she's scared or sad, not pissed.

It's because of what the jacket holds. It holds comfort. Her brother wears it everyday. It smells like him: fast food, motor oil and all. Sometimes, it can be more effective than a hug or a kiss on the top of the head. Plus it's one of Alfred's most prized possession. So, it just fills Alex with a warm feeling that not even I can describe to know her brother cares so much.