What meaning "Chip on their shoulder" takes here?

First, this is a metaphor. Like all metaphors it has a number of possible interpretations. It's not literal, and people do not in fact put a physical chip on their physical shoulder. I'm 70 years old, and I've never seen any actual human being who literally had a chip on their shoulder.

Second, this metaphor refers to any person who seems to take offense easily -- to be seeking out offenses to challenge, in fact. The image has to do with a challenge to "knock this chip off my shoulder," as the first blow in a personal fight. Anybody who said such a thing would have been determined to fight in the first place, and was merely looking for a provoking event. Similar remarks apply to similar metaphors like drawing a line on the ground/in the sand.

Third, it is often assumed (because it is so common and so human) that such irascibility is rooted in a personal sense of inferiority of some sort. It can be a matter of backing the wrong team, or being in the wrong social class, or something more personal. In fact, it is hard to separate personal from social inferiority, and many people don't try. But that's not the only possible meaning, merely a frequent accompaniment to such aggressive display.

I'll go into the semantics here since I have a wee bit of a knowledge of what is being talked about here. If you're from India, you have the perception, thanks to media, that the students who take classes for engineering entrance to make it to IITs are perceived as the so-called 'inferiors'. It is this that is being referred to here. These students are yet to make it to some college and yet they already know that they might be perceived as the not-so-good ones among their peers. I hope I'm clear with my thoughts here.