This is very counterintuitive. A lot of people here favor index investing, and should be saying the odds are with OP. Unless you believe individual stock pickers tend to soar high, but fall extremely low.
No it's not. The only thing index investing with broad market funds (ie, funds such as VTSAX) is just a bit under market returns (because of the expense ratio). Over long time frames, generally speaking, an index does better than a stock picker, because it is
generally speaking hard to consistently pick stocks well over the long term. However, over a short time frame, a stock picker could just get lucky. Which is in line with the last part of your statement.
Look at the .com bubble. You basically could not lose money by investing in tech companies at that time (until, of course, the bubble burst). But a broad market index fund such as VTSAX would definitely have lost to a stock picker who just picked tech companies. I'm not saying that we are experiencing a bubble right now, but at least some people here believe that there is bubbly behavior in certain sectors of the market that can be exploited (or conversely, certain sectors are weighing down the index, so not investing in those sectors will lead to an advantage).
I probably wouldn't have made this bet - not because I don't believe in index investing - but because if the friend wins, he or she is going to become more sure that he or she is able to pick winning stocks consistently (which again, maybe the OP's friend does actually know what he or she is doing. There are certainly people such as Warren Buffet or Peter Lynch who have outperformed the market. But chances are that's not the case).