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human
Why is the statement "Lincoln was a Republican" technically correct, but not historically relevant/accurate?

I got into a discussion with my mother in law about the validity of the claim and I need a simple way to explain how the name "republican" used to be associated with liberalism and the "democrats" with conservatism. I don't quite understand how the switch happened either.

Edit: from what I gather, because the issues of the day were completely different, the Republican party would be considered the more liberal, or progressive party, whereas the Democrats were considered the more conservative party. As a side note, she drunkenly mentioned several times that the Democrats started the KKK. I didn't bother verifying that because it's probably true. But I couldn't make an argument for why the current members of the KKK likely line up with Tea Party, far right Republican ideals. I guess it's difficult to explain why over a hundred years of history has caused both parties to appeal to exactly the opposite types of people than they did at the time.
gpt
TL;DR: It's a big tangle of racial and regional politics, and you should read the whole thing.

Technically, the Democrats and Republicans are the same parties that they were.  However, they've shifted politically, and most of that has to do with the changing nature of race in American politics.

Lincoln was a Republican, and that meant that white Southerners for several generations never forgave the Republican party for the Civil War and Reconstruction.  The Democrats could basically count on the South to always vote with them, or rather, to always vote against the republicans.  For a long time, there was a bloc in the Democratic party called the Southern Democrats that would vote mostly along party lines, but against any kind of racial integration or equal rights.  The shift of the Democrats to be more liberal/progressive was a gradual one, with the New Deal era being a pretty good milestone there.  The SDs stayed conservative and even spun off other wings like the Dixiecrats which were even more so.  The early tears in the fabric of the Democratic party can be seen at the SD walkout during the 1948 Democratic National Convention.

When the Civil Rights movement swung into gear in the 60s, the writing was on the wall for the Southern Democrats and the Democratic party in general.  After the Civil Rights act of 1964 and later the 68 one, as well as the Voting Rights act, there was no way for the SDs to reconcile anymore their party with their politics.  LBJ famously said after signing one of those (don't remember which) "Well, we just lost the South for at least a generation."  Republicans had been shifting around to become the conservative party at the same time the Dems had been moving towards the liberal end of the spectrum.  Republicans began winning in the South again as the Democrats began "betraying" the south with racial integration and SDs began to shift party affiliation.

So we move into the 70s with the Southern strategy of Nixon, capitalizing on the political shift in the South.  By playing up social issues like abortion, he was able to draw some of the last holdouts into the party; it also didn't hurt that, by this time, the last generation who had even secondhand knowledge (their parents' or grandparents' stories of their lives during the war) of the Civil War, and therefore animosity to the Republican party, were dying off.  By the time Reagan was in office, there were not really anymore Southern Democrats, as we knew them.