Why is America virtually the only democracy where the center-right party is assigned red while the center-left party is assigned blue?
Democrats aren't a true center-left party. Historically, the U.S. Dems have very little in common with British Labour, PS, or other European social democracy parties that adopted the color red.
The democrats are still center-left in relation to the political spectrum in the United States, but you are right that the democrats historically are more similar ideologically to say the libdems than labour