Why are the animals in Chinese zodiac in that order?

Each year is assigned an animal according to this cycle: Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Sheep (or Ram), Monkey, Rooster, Dog, and Boar (or Pig).
According to Chinese legend, when the system was created, thirteen animals argued about who got to be first in the cycle of years. The gods (or the Jade Emperor or the Buddha, depending on where you hear the story) decided that a contest was the only fair way to settle the matter. The animals would race across a river and be placed in the cycle in the order that they finished.
The Rat & The Ox: The thirteen animals gathered on one side of the river and jumped in. The rat was a poor swimmer and decided that the best way to cross the river was to ride on the ox’s back. The ox—apparently a little naïve—let the rat on board. As soon as the ox crossed the river, the rat jumped off his back and, in a photo finish, touched the shore first.
The Tiger: Not far behind was the tiger, which had a harder time fighting the river’s current than the ox, but was just strong enough to come in third.
The Rabbit & The Dragon: The rabbit arrived next, explaining that it planned to cross the river by jumping from one stone to another. Halfway across, though, the rabbit hopped onto a floating log and almost got swept downstream. The log somehow washed up on shore.
The dragon, which flew across the river, came in fifth. The gods were curious as to why a mighty flying dragon didn’t come in first place. The dragon explained that it had to stop to make rain for the earth. On the way to the finish line, the dragon saw rabbit clinging to a log and decided to do a good deed and blow the log to shore.
The Snake & The Horse: The horse then came galloping up onto the shore, only to be surprised by the sight of the snake, which had hidden itself wrapped around the horse’s hoof. The startled horse fell backwards into the river, allowing the snake the sixth spot, while the horse placed seventh.
The Ram, The Monkey & The Rooster: The ram, monkey and rooster came ashore together after helping each other across the river. The rooster spotted a raft at the start of the race and agreed to share if the others rowed. The gods placed them in the order they stepped off the raft.
The Dog & The Pig: The dog, which was supposed to be the best swimmer of the bunch, came in eleventh place. It explained that it was so far behind because it hadn’t had a good bath in a while and decided to take one in the river. The pig, which finished last, also got held up when it got hungry during the race and stopped for lunch and a nap.
And the 13th animal that started the race? The cat was also riding on the ox’s back, but the rat pushed the cat into the river, costing it a spot in the cycle. This must be why cats don’t like rats or water to this day