The center used to be way farther to the left. Both parties needed to cater to the working class. Modern conservatism is bullshit.

The conservative Democratic Party base in the south absolutely hated FDR. He won the conservative Dem vote in the north because he promised to bring them out of poverty. But, he was a progressive in conservative clothes when it came to human rights. Conservatives absolutely despised him for being a dedent human, but he did save them (and the rest of the nation) from poverty.

FDR winning as a Dem was the beginning of a 40 year trend of conservative candidates leaving the Dem party in disgust and running as Republicans, especially in the south where a Republican could normally never win (because Republicans were historically the progressives).

Conservatives were stealing the Republican party from the progressives and simultaneously punishing the (normally conservative) Democratic party for not being bigoted enough. These confusing election fights happened throughout the south (and eventually the north) for decades.

By the 60's, conservatives couldn't hide all their deception in elections and just started doing it in the open, calling it their "Southern Strategy" as if they were clever strategists and not lying, racist traitors trying to confuse voters and steal an entire political party.

The party swap was fully complete by the late 60's. Conservatives immediately started taking credit for freeing the slaves, because all conservatives are pathological liars. Always have been and always will be.