I can only guess ....
Why not animal empathy ?
For the core classes, they were trying to keep this skill as exclusive to druid and ranger as possible. Cleric would be just another class that has access to it (albeit only the clerics with the animal domain, but still)... besides, I would wager that there was a congnitive effort to have few things overlap between animal/plant cleric versus druid class to help keep as strong a distinction as possible
Why not handle animal?
If you look at the handle animal skill, the activities described in the PHB's description seem to have a large focus on the idea that the skill is for handling beasts of burden. Yes, it talks about training as well, but just the way that skill is presented it seems almost as if the skill was originall meant for just handling horses, mules, donkeys, etc and was later expanded to include training for other creatures (that's just how it appears to me anyway). So, if that is the case, then the cleric skill to whip pack animals may not be in their interest ;-)
Why knowledge (nature)?
I can see the legitimacy here... i mean, knowing about animals, their habits, their environment, etc does make sense. I could not see granting Handle animal as a class skill withOUT granting Knowledge (nature) as a class skill... so if you had to pick one but not the other, I would have to go with Knowledge Nature simply because it seems it would be prerequisite information (for instance, if you were going to the school of Nature Cleric teachings they would probably inform you about animals prior to teaching you better ways to interact/handle them)
Note, I am not disagreeing with you, I am just offering possible explainations.
