Answer:
First, George's killing of Lennie can be understood as a mercy killing. We know that Curley is a bully who was already angry at Lennie before Lennie accidentally killed his wife. George realizes that Curley is assembling what is essentially a lynch mob. He understands that Curley wants Lennie to suffer as much as possible. Therefore, shooting Lennie in the back of the head while talking to him about their dream farm is a merciful alternative to what otherwise would be a needlessly cruel death.
Second, George must understand that as much as he loves Lennie, Lennie is a threat to the people around him. He doesn't know his own strength, and he doesn't know when to stop once he touches a person. George takes on the painful responsibility for protecting the rest of the world from a person who, although he doesn't mean to be, is a genuine threat to others. Whether it is truly George's right to do this is arguable, but it can also be argued that there are no alternative paths for Lennie.
Step-by-step explanation: