Imaginary Friends

Why do children have imaginary friends? It kind of makes sense. I mean, with real friends you have to put up with flaws, pet peeves, allergies, and you have to share your toys with them. So what I find very odd is that all imaginary friends I've ever had the pleasure of meeting have, in some way or another, had flaws. An imaginary could possibly be "the perfect" friend. You create them so you could make them act anyway they wanted but...
Once a week I babysit a sweet little two and a half year old, toe head, bouncy girl I love very much. I call her Lil M. One night while I was babysitting I suddenly found out Lil M had an imaginary friend she called "Doggy". He was a grey dog that was either the size of a quarter (because she carried him around in one little cupped hand) or he was the size of a Jack Russell Terrier cause when she petted his head it was at the level of her little 2 year-old waist.
After meeting Doggy, telling Doggy to go down the stairs a dozen times, and almost stepping on Doggy I don't know how many times, Lil M told me Doggy needed to go potty outside. She all three of us got on our coats and went outside, and while outside Doggy kept running off. First Doggy would run and hide under my car and we'd try to catch him. Then doggy would run to the front porch and we'd have to chase him. Then Doggy jumped a seven foot fence in the garden but just couldn't seem to jump out so *da da da duh!* super Abby had to go and save Doggy. And after reach time we would catch Doggy Lil M would tell him he was a bad dog and Doggy would be sorry and maybe whimper a bit and Emily would then pat him or hug him and tell him he was a good doggy again, and wouldn't you know it, he'd run off and they'd repeat the whole thing again. After Lil M went to bed I started wondering about Doggy. Why didn't Doggy act like a perfect dog? And why would Lil M keep forgiving Doggy if she knew he was just going to run off again.
Doggy is very real to her so, through what I've seen, she tries to make doggy as life-like as possible. So can a two year old already understand that nothing and no one (not even Doggy) is perfect? Does Lil M know (perhaps only subconsciously) that there is no such thing as perfection? And how can a child (no matter what age) that has never been to church or heard a Bible story take the concepts of unfailing love, repentance, and unconditional forgiveness and apply it to her imaginary friend? Maybe I'll never understand exactly how a child thinks but it sure amazes me how much I always learn from them.