How do I make Git ask for a username and password every time I push?
If you use a Windows system, the Git username and password is stored in a control panel. You can go to Control Panel → User Accounts → Credential Manager:Generic Credentials to delete it.
It seems that users credentials are being cached.
Go to your project, open .git/config and remove the lines:
[credential] helper = store # or helper=cacheCheck git-credential-store for more information.
Edit: OP mentions in the comments that this is happening in Windows, for which, the other answer is more relevant for removing the credentials from the Control Panel.