This could happen even if you have made sure the passwordless ssh between System A and System B (say using either ssh-copy-id command or by manually copying the public key i.e content of the idrsa.pub file on System A to .ssh/authorizedkeys file on System B. If this is happening, one of the reason could be the user home directories.

On System A the user home directory is say /home/tester and on System B, it is /users/tester, then passwordless ssh might not work. Make sure both users have same home directory solves this issue. I observed this case in CentOS machines and on making sure the home directories for users same, the issue resolved.

This error usually occurs when their is no valid public key set for the target server.

First check whether you have valid public and private key generated for the user which you are using.
Keep public key in target server and private key in control server
Get the path for private key and configure it in ansible.cfg file(check ansible docs for this)

Hi there! What happens if you try to connect to your server via SSH?

ssh root@your_server_ip

Did you work through the prerequisite tutorial listed at the beginning of the Ansible installation article?
Specifically step 4.

This one: Initial Server Setup with Ubuntu 16.04

It looks like you don’t have your user’s public SSH key present on the remote droplet that Ansible uses to authenticate? I’m not sure however.

Since you can connect directly, your ansible is defaulting to a different key. Create/edit your ansible.cfg file in your playbook directory and add a line for the location of your key:

[defaults]
privatekeyfile = /Users/username/.ssh/private_key

• From the Ansible master run ssh to the remote target and see if that works:

ssh <user>@<target>

If this works ssh is enabled, move on to the next step.

• Try the following from the Ansible master:

ansible-playbook -i inventory.yaml --private-key=/home/<user_id>/.ssh/id_rsa <playbook>.yaml -u <user_id>

If this fails with the following error, steps listed after the error should fix:

  TASK [Gathering Facts] *********************************************************
  fatal: [x-host.com]: UNREACHABLE! => {"changed": false, "msg": "Authentication failed.", "unreachable": true}
    to retry, use: --limit 

  PLAY RECAP *********************************************************************
  x-host.com   : ok=0    changed=0    unreachable=1    failed=0   

• On the remote host, move/rename the ~/.ssh/authorized_keys file.

• Then from the ansible master run the following:

ssh-copy-id -i ~/.ssh/id_rsa.pub <user-id>@<x-host>

// ssh-copy-id — use locally available keys to authorise logins on remote machine

• This creates an authorized_keys file in the remote server ~/.ssh folder for the <user-id> user.

• Now run the ansible playbook and should work.