Why was Franklin D. Roosevelt pro-intervention?

Yes, effectively, like all US presidents so far.

Excuse the tone, but - Isolationism? The US endeavored, since its inception, to become an empire and intervene regionally and globally. I'm no expert on history, but I do remember reading that even between the lines of some of the Federalist papers... yes, no. 11. It has a steady record of military interventions abroad going back to its very early days:

https://en.wikipedia.org/wiki/Timeline_of_United_States_military_operations

to be a bit tongue in cheek: From the halls of Montezuma to the shores of Tripoli.

So, rhetoric aside, no US government for centuries has been isolationist de facto - regardless of popular sentiment.

Roosevelt and Hitler both were both starting as leaders of a country in 1933. Notice all the mentions of Roosevelt being antiHitler came from much later. One of the first things Roosevelt did was cut the military. Roosevelt was against intervention and with ample evidence that was not going to be a good idea he changed his mind. He simply wasn't ruled by ideology. Most likely what changed his mind was a number of influential Europeans who had viewed the rise of the Nazis as no great risk once they found themselves under German occupation were tortured and killed.

FDR was not an interventionist in the mold of his Uncle Teddy Roosevelt nor did he strive to be. He was very much a "Keynesian" as they are called today in that a big defense buildup as occurred as World War swept the World for a second time in a Generation...his Generation no less...so absolutely there was an economic interest in supplying weapons to those who pay for them leading up to World War 2 as there had been in World War 1. The USA was fully prepared to go to War for its own interests certainly by the Summer of 1941 when Nazi Germany invaded the USSR. This was not an unfamiliar enemy for the US military having fought on the Continent of Europe in the previous World War just 20 years prior. The interests laid out by FDR once war had come to the United States because of the attack on Pearl Harbor were laid out at the Ottawa Conference which I would Google and research if you are interested. When World War 2 ended indeed the USA experienced a massive economic boom...easily the biggest in its History...but that would be a result of WINNING the War and not of the War itself.

I'm going to chime in because I have a point to make I've not seen presented, and it's a great question. (1) Roosevelt was better educated and read than most Americans. (2) This allowed him to recognize the Nazi's for who they were earlier than most of the people he lead.

I would say that Roosevelt was an interventionist firstly because he was better informed. Roosevelt was fluent in German and French. He could both read and write the languages. Most of what Americans knew about Hitler and the Nazi's came from the American Newspapers or the sanitized version of Mein Kampf which was translated and sold in the US in the late 1930's. Roosevelt read both the original German version, and the new English translation of Hitler's first book.

FDR's Library Document 3 (FDR) wrote in longhand on the book’s (Mein Kampf) flyleaf: “This translation is so expurgated as to give a wholly false view of what Hitler really is or says—The German original would make a different story.”

Roosevelt was also in a position to read German and French newspapers in their native languages. Roosevelt read multiple papers, and then read collections of editorials as well as carried on extensive correspondences daily.

Roosevelt believed war was inevitable. He recognized Hitler as a totalitarian bent on world dominance. The choice was simple to support the Democracies of Europe or stand alone when Hitler came for the United States.

There was a side in the debate over lend lease which thought the United States had waited too long and that Britain was already too far gone. They believed Britain would either surrender or compromise with Hitler and that any war materials sent to her would be materials lost. Churchill’s famous we will fight them on the beaches...we will never surrender wasn’t just for domestic consumption.

FDR's biggest job on the onset of the war were considerable.

(1) to Prepare the US Army which when WWII began in 1939 was about the size of Belgium or Portugals military.
(2) To work with the large and irrational isolationist political leadership who made up of roughly half of the U.S. legislature.
(3) To keep Britain and then the USSR in the war, even if it mean breaking US laws.
(4) To silence the very popular American First movement.

Franklin Delano Roosevelt was the ultimate pragmatist. As early as a fireside chat of May 26, 1940, he pointed out that America would not be safe from the calamity that had overrun the Low Countries and France. During this chat, he gave details of a "stealth" re-armament program during his seven years of office that had given America hundreds of new mortars, tanks and planes (starting from virtually nothing) and 215 new ships, including eight battleships. He concluded by saying, "we build and we defend a way of life, not for America alone, but for all of mankind."

In a speech in London, in June 1941, Roosevelt referred to a statue of Abraham Lincoln that had somehow survived the Blitz, and said, "We would rather die on our feet than live on our knees."

Other relevant quotes include:

"It is common sense to take a method and try it. If it fails, admit it frankly and try again. But above all, try something."

And, "if you see a rattlesnake poised to strike, do not wait to crush him until he has struck."

Mark C. Wallace mentioned ideological reasons but there were also economic ones. Free trade was always important for the US including trade with China and other countries in the east Asia. Japanese attempts to conquest China triggered US sanctions, and gradually these sanctions became more and more severe, until Japan attacked. Free trade with Europe was also important, and German conquest of Europe was certainly inconsistent with this.

There is nothing special about Roosevelt here, of course. But the interests of business were always very important for any US government.

I also strongly doubt that most Americans were pro-isolationist.

A reference: Niall Ferguson, War of the world, twentieth century conflict and descent of the West, Penguin Press, 2006.

FDR position was informed by his conviction that intervention was inevitable.

1. In that critical month of May 1940, he [FDR] finally realized that it was probably a question of when, not if, the United States would be drawn into war. Talk about neutrality or noninvolvement was no longer seasonable as the unimaginable dangers he had barely glimpsed in 1936 erupted into what he termed a "hurricane of events." Atlantic

2. Roosevelt argued that the isolationist fantasy of the nation as a safe oasis in a world dominated by fascist terror evoked for the overwhelming majority of Americans not a dream but a "nightmare of a people without freedom." (ibid)

3. Roosevelt was an ardent internationalist and believed that many of the issues within the United States could be solved through a strong international agenda. Study.com

Implicit in the question is an assumption that FDR needed to somehow justify an interventionist stance when OP asserts that the majority of Americans were isolationists. This affects the nature of the question and answer and deserves comment.

• IF there was an isolationist majority, there is still no obligation to defend or justify a minority opinion. The American political system is set up to include minority opinions. (Arguably one of the most important innovations of the American system).

• Isolationism has a long tradition in America, but so does engagement. Washington counselled against entangling foreign alliances, but Jefferson actively supported the cause of Revolution in France and advocated spreading the revolution far and wide.

Other answers have delved deeply into the range of foreign policy opinions. They provide valuable context for the question.