It's even more than just the "emotional victory" of paying off the smallest debts first (which is an awesome feeling, and does help motivate you to continue - no doubt about it.) At one point we had so many payment arrangements for small amounts that it took up all of our take home pay. We had a lot of trouble paying off that first debt because we had no extra money to do it. But once we got that first debt paid off, then we were able to take what we were paying to that first creditor and roll it into our next greatest debt payment. If we had been paying on our largest debt, we wouldn't have been able to increase the payment amount for years, probably. We would have kept spreading our money across all of those mimimum payments, rather than being able to dig in to the next debt with an increased payment.
I do understand that the math works out slightly in favor of paying off highest interest first, but the peace of mind of having one less required payment each month, and a little more wiggle room in our budget if we really needed it was really wonderful. And the difference only works out to a few months more. If I'd done it the other way, my sleepless nights over finances would have lasted a lot longer than they did, and that's worth the few months on the other end.
In the end, you have to find the system that works for you and stick with it. Whatever system it is, it doesn't really matter that much, in the end. Just get started and keep on working on it!