Adding a public key to ~/.ssh/authorized_keys does not log me in automatically

I added the public SSH key to the authorized_keys file. ssh localhost should log me in without asking for the password.

I did that and tried typing ssh localhost, but it still asks me to type in the password. Is there another setting that I have to go through to make it work?

I have followed the instructions for changing permissions:

Below is the result if I do ssh -v localhost.

debug1: Reading configuration data /home/john/.ssh/config
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: Applying options for *
debug1: Connecting to localhost [127.0.0.1] port 22.
debug1: Connection established.
debug1: identity file /home/john/.ssh/identity type 1
debug1: identity file /home/john/.ssh/id_rsa type -1
debug1: identity file /home/john/.ssh/id_dsa type -1
debug1: Remote protocol version 2.0, remote software version OpenSSH_4.7p1 Debian-8ubuntu3
debug1: match: OpenSSH_4.7p1 Debian-8ubuntu3 pat OpenSSH*
debug1: Enabling compatibility mode for protocol 2.0
debug1: Local version string SSH-2.0-OpenSSH_4.7p1 Debian-8ubuntu3
debug1: SSH2_MSG_KEXINIT sent
debug1: SSH2_MSG_KEXINIT received
debug1: kex: server->client aes128-cbc hmac-md5 none
debug1: kex: client->server aes128-cbc hmac-md5 none
debug1: SSH2_MSG_KEX_DH_GEX_REQUEST(1024<1024<8192) sent
debug1: expecting SSH2_MSG_KEX_DH_GEX_GROUP
debug1: SSH2_MSG_KEX_DH_GEX_INIT sent
debug1: expecting SSH2_MSG_KEX_DH_GEX_REPLY
debug1: Host 'localhost' is known and matches the RSA host key.
debug1: Found key in /home/john/.ssh/known_hosts:12
debug1: ssh_rsa_verify: signature correct
debug1: SSH2_MSG_NEWKEYS sent
debug1: expecting SSH2_MSG_NEWKEYS
debug1: SSH2_MSG_NEWKEYS received
debug1: SSH2_MSG_SERVICE_REQUEST sent
debug1: SSH2_MSG_SERVICE_ACCEPT received
debug1: Authentications that can continue: publickey,password
debug1: Next authentication method: publickey
debug1: Offering public key: /home/john/.ssh/identity
debug1: Server accepts key: pkalg ssh-rsa blen 149
debug1: PEM_read_PrivateKey failed
debug1: read PEM private key done: type <unknown>

Then it asks for a passphase after the above log. Why isn't it logging me in without a password?