Why did Western nations use appeasement with the Axis powers?

One reason the Allied powers pursued a policy of appeasement is that they were weary of war after the bloodletting of the First World War and were reluctant to pursue any policy that seemed likely to bring about another conflict. Having lost vast swaths of their male populations, they were understandably fearful about entering into any new war.
Another reason was that Hitler, while repugnant to many Westerners, was seen by many as the lesser of two evils when compared to Joseph Stalin in the Soviet Union. Communists advocated global revolution in a way that Hitler did not, and many saw Hitler as a valuable if dangerous bulwark against the Soviets. This is why they were so horrified at the announcement of the Nazi-Soviet non-aggression pact in 1939. In fact, many British, American, and Frenchmen shared Hitler's views on race and anti-Semitism.
In 1938, with the crisis over the Sudetenland breaking out, the British army was not seen as capable of dealing with the threat posed by the Nazis. The Sudetenland was not worth going to war over, but without it Czechoslovakia was seen as impossible to defend. So essentially, the Munich Conference, where the much-reviled Neville Chamberlain claimed to have achieved "peace in our time," was held over a territory seen as a lost cause by many strategists.
Another reason that Europeans pursued appeasement is that they underestimated Hitler's capacity for boldness and dishonesty. When he promised no further aggressions at Munich, some believed him, if only because, as mentioned above, they had little choice.
Finally, the United States, which, as a massive industrial and financial power, was essential to any war against the Germans, adopted an isolationist stance in the 1930s. "America First" advocates, many of whom were genuinely sympathetic to the Nazis, were vocal and prominent in the United States. Others in Congress attempted to restrain President Franklin Roosevelt, whose instincts were always toward involvement in global affairs. Without the backing of the United States, the European powers played with a weaker hand in dealing with Hitler's aggression.
https://www.iwm.org.uk/history/how-britain-hoped-to-avoid-war-with-germany-in-the-1930s

https://www.spiegel.de/international/europe/the-road-to-world-war-ii-how-appeasement-failed-to-stop-hitler-a-646481.html