Why am I getting permission denied?
Because APT requires root permissions (see the error: are you root?) and you are running the tasks as david.
Per these settings:
become: true
become_user: david
become_method: sudo
Ansible becomes david using sudo method. It basically runs its Python script with sudo david in front.
the user ‘david’ on the remote box has sudo privileges.
It means david can execute commands (some or all) using sudo-executable to change the effective user for the child process (the command). If no username is given, this process runs as the root account.
Compare the results of these two commands:
$ sudo whoami
root
$ sudo david whoami
david
Back to the APT problem, you (from CLI) as well as Ansible (connecting with SSH using your account) need to run:
sudo apt-get install sqlite3
not:
sudo david apt-get install sqlite3
which will fail with the very exact message Ansible displayed.
The following playbook will escalate by default to the root user:
---
- name: Testing...
hosts: all
become: true
tasks:
- name: Just want to install sqlite3 for example...
apt: name=sqlite3 state=present