Winston Churchill opposed Neville Chamberlain because Churchill thought war with the Germans was inevitable and wanted the country to prepare for it by aggressively rearming.
From almost as soon as Hitler took power, Churchill was warning of the dangers of Germany rearming and forcing another war. Chamberlain, however, believed it was possible to appease Hitler by letting him have more territory in Europe. In Chamberlain's defense, Great Britain's people were still reeling from the costly blow of World War I, in which vast numbers of lives were lost. Nobody wanted another major war fewer than 20 years after the last one, which was burned into many people's memories as a horror.
Chamberlain hoped that giving Hitler the Sudetenland in Czechoslovakia would finally satisfy him and avert a war. As history has shown, this was wrong. Churchill was right in his assumption from 1933 onward that Britain needed to prepare for another war.