The only way it would change something is if it would make your total skill points go under 350.
Every skill raises faster when you have less than 350 skill points.
The disco thing can be explained like this :
lowering anat makes healing harder for the pet so it gains healing skill points faster. I may be wrong but it would make sens.
And in the other hand, without animal lore, no control and that could be a bother as then you can't use the new tamed pet to kill the last one or even one of your own pets or bring it to the zoo to donate except if you can ride it etc ...