when? if you're thinking of halo legends, then those weren't odst's. they were spartans
I think he's referring to the story "Dirt" in the book Halo: Evolutions. A bunch of ODSTs went rogue to get a Forerunner artifact that they could sell for money. They fought with the loyal ODSTs, including the Rookie from H3: ODST, and the Covenant force attacking the planet they were on. Rookie listened to a fellow ODST, in the last moments of his life, tell the story of this mutiny. After he explained the situation to Rookie, the dying man told him to run, as he was going to set off a nuclear weapon as the traitors and Covenant swarmed his position. Rookie was just outside of the nuke's range as it went off, killing thousands of traitors and Covies and destroying the artifact the rogue ODSTs were looking for. Anyway, why does anyone betray a cause? Probably because they think that the situation doesn't benefit them and turning against that cause in favor of personal gains took hold. In this case, the ODSTs thought that they could sell the artifact for a massive amount of dough that they could live high off of.