Hop on Pop, besides being a brilliant learning tool for children, has the added dimension of a hidden historico-political message. Pop is not only the literal father of the hopping children, but a representation of monarchy. Kings are after all seen in a paternalistic role towards their countries. More specifically, Pop is Charles the First of England, and the "hoppers" represent Oliver Cromwell and his Roundheads, who not only hopped, but chopped the monarchy out of power in the 1600s.
When Pop declares "Stop. Stop. You can not hop on Pop," this is one of Seuss's most brilliant political statements. Here, the monarchy, now in the person of Charles the Second, is throwing off the rule imposed by Cromwell, and restoring to its rightful place the monarchy. "Pop" is asserting his paternal right and duty, his droit de seigneur." Le roi est mort, vive le roi!