Calvin Coolidge, the President of the United States at the time, chose Andrew Jackson to be the figure who adorned the Twenty-Dollar Bill. Prior to the New Left historiography of the 1960s, Jackson was not demonized and was seen as a figure who symbolized national unity and popular government. Coolidge especially appreciated Jackson for putting down the early attempts at nullification and secession in the 1830s and for asserting that these practices violated a strict reading of the Constitution.
Though Coolidge was a Republican loyalist, there was bipartisan, national support for Jackson in the 1920s. Many people who fought in the Civil War, on both the Union and Confederate side, were still alive. Given the recent memory of the Civil War, the leadership class sought a way to build a postbellum Union characterized by reconciliation, harmony, and national unity. Jackson was a great symbol of this, since many rightfully pointed to his love of the Union and his hatred of both Northern and Southern sectionalists in the 1830s. Honoring Jackson was seen as a way to bridge the traditional divide between Northerners and Southerners and to unite the country around shared principles of liberty under the federal Constitution.
But, by all means, continue to just assume that this was an entirely unreasonable decision with no rhyme or reason to it besides "racism." New Left "historiography" is not really history at all, particularly as it relates to Jackson, who adopted a Native American as his son and treated the slaves of his household with as much respect as anyone could be treated who was confined to that sordid station. He was paternalistic as it relates to the races, but was not any more racist than Abraham Lincoln, Thomas Jefferson, or George Washington.
The best reason to support removing Jackson from the $20 is simply that he despised inflationary, fiat currency that was not backed by gold. He would want nothing to do with the Federal Reserve, given his successful war against the Second National Bank and its inflationary policies.
killing native americans isn't very christian of you, mister luther