This may sound like a stupid question, but here goes…
Most members of the KKK are (if in name only) Christians. If so, why would they go around burning crosses, which is Christianity’s holiest symbol (maybe aside from the crucifix)? After all, if I (being Jewish) were angry at another Jew, I certainly wouldn’t go burn a Torah on his lawn. Why the desecration of their own holy symbol to spread a message?
The origin is in Thomas Dixon’s racist, KKK-glorifying novel The Clansman, popularized by D.W. Griffith’s seminal film The Birth of a Nation. Dixon falsely attributed the old Scottish custom of burning crosses to summon the clans to war to the Reconstruction-era KKK. The real Scottish clans had used the X-shaped cross of St. Andrew, but Griffith and subsequent Klansmen didn’t know that and consequently used the familiar T-shaped Latin cross.