Why did Angel start smothering Wesley with a pillow?
Well because it's a TV show and when you want to kill someone who's laying in a hospital bed in a TV show you use a pillow of course.
It was either that or inject some suspicious fluid into his IV drip. There are certain traditions to follow you know.
If we want to analyze this as if it were reality though, the screaming and shouting were probably along the lines of when someone says, "If he/ she does that ever again, I'll kill them."
They don't really plan on killing the person...they're just really cheezed off and need to vent.
I mean if one of my friends endangered one of my loved ones in some misguided attempt to keep them safe from me, whom they know and certainly should trust to never hurt someone I care for no matter what, well yeah first thing I'd do is haul off and break their nose and then proceed to tell them very loudly what an idiot they are while using as many expletives as possible.
If it were reality I wouldn't blame Angel at all.
I'd also want to lecture all of them on the need to communicate about what the hell they did/learned that day so this type of stuff didn't happen. But as my wife tends to have to remind me oh so patiently while I'm screaming at the TV, "Honey, that would make too much sense and if they actually did that it wouldn't be nearly as entertaining."