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 - 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).