permission denied on authorized_key file

It might be SE Linux. If the context of the file isn't correct, running this as root should fix.

restorecon -Rv /home/user/.ssh

Also check the permissions on /home/user/.ssh aren't wide open. SSHD is quite particular about this.

chmod 0700 /home/user/.ssh

I had a similar issue, and in my case the cause was wrong ownership of both the .ssh directory and .ssh/authorized_keys file. To fix that, in /home/user as root:

chown user:user .ssh
chown user:user .ssh/authorized_keys

Your authorized_keys file should have permissions rw-------. Run:

chmod 600 ~/.ssh/authorized_keys

And just as a note your private key (typically id_rsa) on the client should have the same permissions.