Why does Anzor walk away?

Because fundamentally even though he's an abusive person he can't kill...especially a child. Although he's a bully, he's weak at least in Ivan's eyes... you can see him visibly uncomfortable during the ice-rink scene.

But that doesn't mean he isn't capable of sacrifice, even heroism.

His greatest hero is John Wayne "The Duke"...he even has him tattooed on his back. When we first see Anzor, he's watching a Wayne movie (The Cowboys) where Wayne is walking away only to get shot in the back.

He says...

My version of The Cowboys, it was only 10 minutes long.

No John Wayne getting shot. Because it was for kids, they left that part out.

I didn't know this... until I arrive in America... and see it on TV for the first time.

I hate it. I want my 8-millimeter back.

Because on that one, the Duke lives.

He even tries to get Oleg to provoke him, as Oleg had at the beginning of the movie...

Say something bad about the Duke. Let me hear you call him a faggot.

But Oleg doesn't...

Joey even says...

If you do it, I swear to God... you better fucking swallow a bullet.

There's no fucking way you're going to be able to live with yourself!

Anzor realizes that he can't kill, removes his shirt to show off his tattoo of the Duke...and walks away.

Maybe his version of The Cowboys will be cut off like his old movies and we won't see Anzor/Wayne shot in the back... maybe he can walk away.

But... just like the real movie... he can't escape his fate.

Director Wayne Kramer says...

Anzor represents the failure of the American dream, or the failure for someone to achieve the American dream as mythologized to a young kid back in Communist Russia. Anzor is a life soured and lived unfulfilled.

He did the decent thing by saving Mila’s life and he paid a steep price for it, losing his standing in his uncle’s criminal enterprise. As such, he resents Oleg because he projects his own failures and shortcomings on the child whose life he saved, along with Oleg’s mother. Anzor did a selfless thing in marrying and saving Mila, but can’t come to terms with the consequences, so he takes his rage and frustration out on the two of them.

Anzor also lives with an idealized version of America in his head.

It’s a version where heroes like John Wayne don’t get shot in the back. The ‘good guy’ always wins in the end. He fails to understand the selflessness of Wayne’s character Wil Andersen in The Cowboys that gets him shot in the back at the end of the second act?—?that’s he protecting the kids (which is ironic since that is what Anzor did for Mila when he stood up to his uncle).

Anzor has this epiphany on the ice rink at the end and finally understands the power of Wil Andersen’s sacrifice and it’s like a white hot light hitting him. He decides to make a stand against his uncle and comes full circle on his original selfless act

He decides to go out as the good guy, just like John Wayne?—?rather than commit evil and kill a child.

^Medium.com