The Word of God was wise when it chose sheep as a type of lost man. Sheep are such simple animals. When you find a lost sheep it looks lost. It knows it's lost. You know it's lost. There is just a simple openness and helplessness about lost sheep. So when God says in Isaiah 53, "All we like sheep have gone astray ..." it isn't really hard to relate the picture to lost man.
On the other hand, if He had said, "All we like cats have gone astray ..." we would have a totally different problem. Cats just don't like to think of themselves as strays. They never seem to be able to admit that they have made a mistake. There is a certain air of pride about a cat that sheep just don't have. The cat may know that he is lost but he is not going to let you know that he is. Cats seem to always be saying, "I know who I am and what I am doing, and it is just exactly what I intended." He can fall in the pond, nearly drown, and barely make the bank alive, but he will crawl out, look you square in the eyes and say, "I meant to do that."
Once you were wandering like lost sheep. But now you have turned to your Shepherd, the Guardian of your souls. (1 Peter 2:25)