In
GTA: San Andreas there's a middle-aged DJ who mocks the young female DJ of a different station by saying "Listen honey: get over it." I bring this up because I really want to yell this at Chloe sometimes. Yes, you don't "get over" childhood trauma and, in as much as PTSD and arrested development from said trauma are mental illnesses, Chloe is actually mentally ill and not pretend mentally ill like SnP and her like.
Even so, I think I can best sum up why she can be annoying to read sometimes with a recent example. Here are #463 and #468 (sorry for the wordy examples):

As you can infer, Pepper is going through some trauma himself and is just barely holding it together. His entire existence is about helping others by talking but he doesn't have anyone to talk to about his own problems.
That second strip is the only time I can think of where he reaches out and asks someone for help, but Chloe is so wrapped up in herself she doesn't even notice. She doesn't seem to have any theory of mind -it doesn't even occur to her that Pepper might have his own shit to deal with. Bear in mind she woke him up at 3AM for this.
If this were any other comic I'd dismiss Chloe as completely unsympathetic here, but it should be pointed out in fairness that Halo Head (the place) was designed for the sole purpose of helping Chloe. I can't begrudge Chloe for expecting the world to revolve around her because Halo Head is
supposed to. I just feel bad for Pepper and sometimes Clair, that's all.