Why gas turbine is trip on excitation failure?

Answer 1

The excitation system puts the load on the generator, so if it fails, the generator is liable to overspeed.

Think of it as the gears on a bicycle, where your legs are the power source, the gearing is the excitation system. If you're riding along, and suddenly your gears fall off, your legs will start to move very fast. You might hyper extend your knee, your foot might slip off the medal, you could hurt yourself in a bunch of different ways because you expect the resistance to be there and it is suddenly gone. The same applies to a generator - it's designed to run at specific speeds. Going significantly faster can cause all kinds of problems.