I think that both killings result from Lennie wanting to touch something "soft" or "purdy." Steinbeck constructs both killings as accidental, something that was motivated by Lennie's love of something beautiful and not recognizing the limits in appreciating it. Presumably, Lennie killed the puppy by petting it to an extent and force that the animal could no longer endure. The same with the mouse that he was petting in a manner that was beyond the capacity of the creature. In the same way, Lennie kills Curley's wife because he keeps holding on to her hair as she tries to violently push away. I think that Lennie's hands, themselves, might contain a symbolic significance in each of these murders. As seen with Lennie breaking Curley's hand, the size of his hand is enormous. Equally enormous is his strength. Simultaneous with these realities is Lennie's love of childhood elements. Lennie is fascinated, like all children, with the sense of touch. This tactile sensation is how he is able to interact with his world on a more significant level. The interesting element here is that there is destruction that results with such interaction. Lennie cannot but help destroy that which he touches. This dynamic of wanting to interact with the world in a more meaningful manner through touch, but invariably bringing destruction as a result is what makes Lennie's character both compelling and sad at the same time.