Here's why this was a major issue:
* No known force strong enough: Scientists couldn't identify a force powerful enough to overcome the immense resistance of the Earth's crust and mantle to move continents.
* Missing explanation for movement: The hypothesis lacked a clear explanation for how continents could plow through the ocean floor without leaving significant evidence of their movement.
This lack of a mechanism made the idea of continental drift seem very improbable to many scientists at the time. It wasn't until the development of the theory of plate tectonics in the mid-20th century, which explained the driving force behind continental movement (convection currents in the mantle), that the objections to continental drift were finally addressed.