Just created a new user B on CentOS 6.8 and set public key of Ubuntu 16's user A to B's authorized_keys. Works fine. NOT ask password through ssh connection.
After change B's home directory (in /etc/passwd/ : /home/B > /user/B), ask B's password. Try to connect from A to B through SSH and permission is same on /home/B and /user/B.
Is sshd's default root path /home/?
Thanks a lot! Jakuje. You're right and solved problem.