Cause they didnt want a new war after they had the first one. They saw the cost of the first one and didnt want that again. They hoped with giving Hitler what he wanted he will be peacefull.
Appeasement was popular for several reasons. Chamberlain - and the British people - were desperate to avoid the slaughter of another world war. Britain was overstretched policing its empire and could not afford major rearmament.
