Angular, BehaviorSubject, Observable - Need help understanding the observable

Hello Everybody,

Angular project:
StackBlitz: Sample test code

I been trying to understand the topic of BehaviorSubject & Observable by using a simple login application with no success. For some reason i cant seem to get my head round the observable world.

the simple application I put together logs a user in by clicking a button and if successful it sends them to the App-home if not bsack to the login page but nothing seems to be working.
I created the code on stackblitz and wondering if someone could have a look and correct my mistakes with some comments for understanding.

any help you can provide would be greatly appreciated.