I don't care if my puppy can hunt or not, but Sims should be able to teach them basic tricks, like "Sit", "Sit Up" etc. I tried looking through Retuner Settings, but I couldn't find anything.

This would be the equivalent of allowing children to do things they were not programmed to do. i believe that the animations for baby animals learning tricks do not exist, so they would stretch out and distort horribly during the process if made to do so. A mod that allowed for these things would have to include some new animations for them so as not to break player immersion as they get distracted over what would otherwise be a horrible looking scene before them.

We are fortunate enough to have the Children Can... series of mods to use, but more typically there isn't much intersection between mod developers and animation designers so this kind of thing is not as common as it might be.