Why?
Because if the Japanese controlled the Dutch East-Indies, this would give them resources to offset the oil embargo of the United States. The US embargo was placed on Japan in the first place because Japan was using it's military power aggressively in an attempt to monopolize East-Asia. Since Commodore Perry the United States has had a huge strategic and economic interest in East-Asia. Also Japanese seizure of the East-Indies would isolate the United States from their bases in the Philippines. The fact that Japan would be attacking the United States's last ally (Great Britain was co-administering Indochina in 1940) is only the tip of the iceberg.
We did nothing when Britain itself was under imminent threat of invasion from Germany.
I'm sorry, this is untrue, the Americans did quite a lot before they entered the war. I apologize for the blocks of text.
An "imminent threat" of invasion means that the invasion is going to happen for sure. Sea-Lion never did happen, it became virtually impossible in 1940, in large part due to the fact that the United States was supplying Great Britain with all sorts of materials, most significantly planes to help win the Battle of Britain. The United States was doing so much to help Britain, while technically remaining at peace, that the leadership of Germany felt that the United States was de facto their enemy and was imminently going to join the war against them.
A closer look at Aircraft Armaments, perhaps the most decisive sector of Britain's defense, shows how American involvement was decisive before it officially entered the war.
TLDR: In 1940 Great Britain was able to domestically outproduce Germany in Aircraft. In 1941 the United States was able to outproduce both Britain and Germany (individually) in aircraft while technically remaining at peace until 07 December.
Fact is that at the time the US population didn't want to get involved in the world war. Had Germany not declared war on us we probably wouldn't have involved ourselves more in the European theater, and had Japan not attacked Pearl Harbor we probably wouldn't have done much in the Pacific either.
In such counter-factual scenarios, we will never know for sure. Past precedent contradicts you, the Germans did not declare on the United States in World War 1, effectively unrestricted submarine warfare caused Wilson to join the Allies. I consider the Zimmerman Telegram to be silly pretext, embarrassing for Germany but meaningless on it's own.
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