Why Better WP security plugin returns 418 I’m a Teapot “error”?

That is the response it gives when it you have the “Intrusion Detection” or the “Login Limits” features enabled, and the plugin has intentionally blocked you. It can block you by either username or by IP address.

The plugin can be configured to email somebody when a lockout occurs with the reason for that lockout. I suggest that you use this feature to determine the issue.

However, if you want it to stop, then you will need to reconfigure the plugin to, basically, not do that.