ssh passwdless failed after add id_rsa.pub to remote machine

My remote machine has 2 users one is root and another is Alexander. And I create a new user fit with root user.

# adduser fit

And I scp the id_rsa.pub of my home machine to fit@remote_machine and add to the authorized_keys.

fit$ cat id_rsa.pub >> ~/.ssh/authorized_keys

But, after that I still have to input the passwd to login remote machine

home$ ssh fit@remote_machine
fit@remote_machine's password: 
Last login: Fri Apr 15 09:55:34 2016
fit@localhost.localdomain:[/home/fit]

But, what really made me puzzled is that I scp the id_rsa.pub of my home machine to Alexander@remote_machine, and add to the authorized_keys of Alexander@remote_machine. And I can login the remote machine without passwd:

home$ ssh alexander@remote_machine # login without passwd
Last login: Fri Apr 15 09:58:19 2016 from 27.46.137.183
/etc/profile:fc:80: no such event: 1
Alexander@localhost: ~

Thanks!