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Believe it or not it hasnt always been this way. Social progressive stances historically were found in both parties and so were socially conservative ones. In fact for most of American history the greatest indicator of social stances and policies wasnt your party but rather where you lived geographically (with the south and rural midwest being dominated by conservatives and urban coasts and Northeast dominated by Progressives). Your political party was usually more of an indicator of economic policies you supported. Depending on what period of American history youre talking about Republicans have always traditionally been in favor of big business interests, in the past they wanted to use income for the government on internal improvements like railroads while democrats wanted to use revenue to reduce taxes and tarrifs and usually they supported inflationary policies like the silver dollar and greenbacks.
Many of Americas most notable progressives were actually Republicans like Theodore Roosevelt who was anti trust and in favor of policies like the 8hr work week aminimum wage banning child labor etc. In 1912 however the Republicans backed Taft, Teddys successor, who represented the conservative wing of the party and thus began the process of many progressives leaving the republican party. (Remember this process happened very slowly and even later on youd still have Republicans like Eisenhower who were very much in favor of a welfare social safety net 40 years later).
Anyways, remember when I mentioned Democrats embraced inflationary policies? That was around the time they merged with the populists party and in general Dems were more pro union (since they believed unions and companies needed to settle workers rights issues rather than rhe government doing so). Well combine that with progressives leaving the Republican party and a Great Depression and you get: FDR. FDR is pretty much as close as ypull ever get to a socialist American president. His New Deal brought out tons of social welfare programs to deal with the depression, he reshapes the Democratic party, then his successor Truman desegregates the federal govt (something that was first put in place by another Dem president Wopdrow Wilson). Eisenhower also takes a role in favor of civil rights but the guy frankly was appealing to members of both parties anyways. So FDR is what made the Democrats into the leftist party leaving the GOP as the capitalist or right wing party. Then in the 60s Lyndon B Johnson passes the Civil Rights Act of 1964 (there were others before this but this is the one that matters). Conservative Democrats break from the party to become the Dixiecrats who get swooped up over time by the GOP thanks to the southern strategy. Meanwhile social progressives had been slowly leaving the party and moving towards the Dems for decades. Even Black voters had moved from the party if Lincoln to FDR (because of his pro union stance) and cause of Johnson. By the time you get Reagan in the 80s we have our modern political system in America. The GOP had purged out its progressives and they went to the Dems and the Dems increasingly progressive social stances caused its own Conservatives to walk out on them amd join the GOP. As a result you now have the two parties of today who are more polarized than they have ever been in US history. I hope this answered your question, I know its a lot but you said you werent American and so I wanted to give as much context as possible.
It dates back to the French Revolution and the National Assembly. Those who wanted to retain more traditional elements in the new constitution (i.e. the more conservative) would sit on the right hand side of the assembly, while those who wanted more radical reform would sit on the left hand side. >

Huh. Thanks. I never knew that.