Are Android phones too big?

I have considered switching to Android a number of times, particularly given Apple’s poor icon design choices in iOS 7. But I don’t think I could use some of the larger Android phones very well. I have nothing against them, but I don’t think they would work well for my use case. Let me give you a funny example of using my iPhone one-handed. I have two parrots that often like to join me on the couch when I watch TV. They cannot be allowed near each other as one of them detests the other one and will attack her if she gets too close to him. So I keep one on my arm while laying on my side, and the other one nestles in my hand.