Why might a society choose to change their political system?

The current political system (government) of the society may have become corrupt, oppressive, out of touch with the people, or it may have broken down beyond repair.

There could be numerous reasons to change the system. Whether it is making 'minor adjustments' or 'repairs' to the system to help it work better, or changing the entire thing because it just didn't/doesn't work like it was supposed to.

The political system is the engine of the government.

Just like the engine in an automobile needs to be worked on from time to time to keep it running smooth, it may also need completely replaced when it has broken down beyond repair.