The advantage to kicking off to start OT is that, if your defense can force the other team to go three and out, you can get better field position.
Think about it. The receiving team gets a kickoff, which will put them more or less at their own 20. If they are stopped around their own 30, they'll punt and the other team will get it somewhere around their own 35, with a chance to get 10 or more yards (or even a TD) on the punt return. And then even if they also go three and out, they'll be able to pin the other team really deep in their own territory.
I still wouldn't elect to kick if I was the coach, but it's not as big of a disadvantage as many people think it is.
FYI, for those who are asking, college overtime rules work sort of like a shootout, like so:
1. Winner of the coin flip elects to go on offense or defense first. Defense is the better choice because each team gets one offensive possession per OT period regardless of what happens.
2. Team 1 goes on offense, starting from their opponent's 25 yard line. Once that team scores or turns the ball over, they give it to team 2.
3. Team 2 then goes on offense, with the goal of scoring more points than Team 1 did. If they score the same number, it goes to a second overtime period.
4. Starting with the third overtime period, if you score a touchdown, you must try for a 2-point conversion.
5. There is no limit to how many overtime periods are played.
Turnovers are basically fatal since each team starts within field goal range.