Because they are unique and have characters, not just simply cats and dogs and horses.
they are also easy to tote around have little catchy tunes (the happy tune when you clean up it's poop gets stuck in my head a lot <.< )
I took my V3 and V6 (both asleep) with me in a quick car ride to go to the store with mum. I put them a lanyard around my neck without thinking xD
It's so easy to clean up after them and feed them, feeding my kitten is hard (she has special food where you have to add some water and too much water makes it expand like crazy and then bam the cat food cat is so big,one piece is the size of a baseball. Scary o.o ) And ugh cleaning up after my cat.....nightmare. But on tamas, all you have to do is press some buttons, and bam, poo gone, tama fed.
This might sound crazy, but I don't think of them as electronics or pixels with a circuit board in a piece of plastic. I like to think that they're living things.