Almost every system can be disengaged and overridden by the pilots. But it's not as easy as pressing the button most of the time.
They have to identify which system is causing the plane to behave in such manner, and how to overcome it. They have a huge manual and have to follow instructions on how to disengage a sensor, override some safety system, engage auxiliary systems or combination of those. And that can take many minutes or even hours with secondary systems and unusual problems.. It's immensely complicated and sophisticated system. Like a massive computer system that controls physical systems. And not very easy to master or know how to respond to obscure issues.
Some primary systems are easy to disengage, like auto pilot abort landing, etc.
And you are talking about a plane taking sudden nose dive and limited time to respond!
How do you think all these planes crash into mountains, miss landing strips and so on?
No need to mock the pilot based with circumstantial evidence