I made the point about boarding early to suggest that "more time" wasn't going to solve this particular problem--unless perhaps the parents expected the plane to remain on the ground until the child's regular naptime rolled around.

The bottom line is that airlines reserve the right to boot anyone off an airplane who is disrupting orderly operations. Sometimes they take it too far, but in this instance they were correct to remove the parents and child. And the parents were entirely out of line to think that they had any right to hold up the flight to accomodate their out-of-control child.