Being cool was Justin's answer for starting up. While it may be honest, he could have added other thoughtful answers. More details on his first YC interview would also be interesting, instead of saying that he didn't say much at the interview.
1) you can work on what you like, and in a way that you like 2) it's higher beta, meaning the top outcomes are higher than working for others. 3) it is a chance to immediately start working on a high impact idea that could change society. There are other ways to work on high impact ideas, but often times you need to put in a lot of time paying dues to get to the point you can work on them. 4) if you are successful, it can be a source of mainstream fame (think Richard Branson) -- if you care about this at all.
Here's a summary I wrote of my YC interview that I did with Emmett back in 2005: http://areallybadidea.com/34320844