Factsheet
Because FDR belonged to a school of thought that felt that the primary goal of US foreign policy should be to promote and defend US ideals abroad.
I know the common narrative is to divide US foreign policy thought into two camps: Isolationist and Interventionist, but I've always found that an inadequate tool.
Much better is Walter Russell Mead's four-way division of American foreign policy schools:
- Hamiltonian - Primarily interested in promoting American enterprise at home and abroad.
- Wilsonian - Primarily interested in promoting American values throughout the world.
- Jeffersonian - Primarily interested in protecting American Democracy at home from possible foreign enemies. Big proponents of Realpolik.
- Jacksonian - Distrustful of any foreign agreements, treaties, or responsibilities. Motto: Never start a fight, but always finish it.
Mead views every US foreign policy decision as a struggle for some kind of consensus between these four communities.
If there's no credible threat to (both) American commerce and American values abroad, and seemingly no imminent threat of attack, then the Jeffersonians and the Jacksonians tend to prevail. This looks like "isolationism". This is the condition that prevailed until the run-up to WWII.
However, once England was under threat, that's a whole different ballgame. They were at the time the US's biggest ally and trading partner, which gets the Hamiltonians wanting intervention. The Nazi/Fascist takeover of the democracies of the continent had the Wilsonians wanting intervention. However, getting a consensus for actual military action would take either a threat to the homeland to get the Jeffersonians on board, or some kind of attack on the US to get the Jacksonians on board.
FDR himself came from the Wilsonian branch of the Democratic party. Wilson himself had been the last Democrat to ascend to the presidency, and FDR was an early and avid supporter (which was how he got a gig as Assistant Secretary of the Navy). In that position he spent years enmeshed in a Hamiltonian environment (the Navy has always been a hotbed of that philosophy, as the Army tends to be strongly Jacksonian), and had many political ties there.
However, without an attack or credible home threat, there could be no consensus for actual war. So his administration was forced to do what it could short of that (including subtly poking the totalitarian tigers, in hopes they'd lash out).
FDR position was informed by his conviction that intervention was inevitable.
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
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)
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.
How come FDR sent lend lease to Britain and other countries before the U.S. got involved in WWII? My thinking says that Germany and Japan would have become more of a threat if the U.S. didn't give aid against them.