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In all seriousness, I actually don't like a pet raising game. That doesn't mean, however, that I won't like it ever. I just haven't found one that seems to be enjoyable. I also haven't played a lot of them.
Last game I played was Monster Galaxy on Facebook. It started off good. It uses the Zodiac to determine monsters weaknesses and strength. Certain zodiacs are better and worse against other zodiacs, which I thought was kind of creative. What turned me off was the complications in raising your monsters. This same complication is what turned me away from modern RPGs nowadays.
For example, do you know that feeling when you first started playing an RPG, when you go to the character screen, and presented to a screenful of abilities and their trees and categories, and each has a 200-word long description of what it does? First thing that goes through my head when I see that is "ah wtf". That's when I throw away the controller.
I enjoyed dota because each character only has 4 skills. I don't enjoy LoL (even though the same thing as dota) because of the customization. I enjoyed old-school RPGs because all you need to care about is your stats and items. I don't have to decide creating a Fire or Ice or Lightning mage. OR deciding between Uber-Fire-Magelord skill tree vs Fire-Elemental-Summoner-WizardKing skill tree.
Now, you combine that with pets. Imagine having 100 pets and each one of them has that many abilities and customization. I don't have time for that.