Why did the western democracies fail to stop Axis aggression in the 1930s?

That's a darn good question. Certainly Hitler might easily have been stopped before his evil career reached full flower, and millions might have lived to grow old and die in their beds instead of finding an early death.

Basically France and Britain lacked the political will to do so. They both had a belly full from the first war, and wanted no more of it. The people of the US, disgusted with the result of the first war, wanted as little involvement as possible in the endless, dreary, greedy, violent European situation.