The context is below.
Bansal is the famous coaching center to clear Engineering Entrance test. Bansal students had a chip on their shoulder, even though they weren't technically even in a college
The meaning for the phrase chip on their shoulder is a form of physical challenge, inviting opponents to knock the chip off and so provoke a fight. I can understand its meaning refers to they are so much alert to face any question or puzzle related to engineering entrance test. But why author added the clause even though they weren't technically even in a college? It confuses me. Does it mean only students those goes to college should pocess that kind of attribute or mindset?