The theories of continental drift were extremely controversial when first introduced by Alfred Wegener circa 1920. Wegener showed that the Americas and Africa fitted together nicely and suggested that continents move. Alas, his rationale for how this might occur wasn't correct and he was lambasted by the scientific establishment of the time, particularly by Cambridge geophysicist Harold Jeffreys, and the entire concept of continental drift was discredited. It was not until the 1960s and 1970s that ideas of continental drift came to be accepted as the norm, when new theories of plate tectonics were advanced.

Newtonian physics to relativity. Geocentricity to heliocentricity. Early chemistry to more modern atomic theories, and then to quantum theories.

There are also non-scientific examples, like streetcars to automobiles in the early 19th century.

Paradigms are usually theories in which an older scientist who has invested a great deal in the old paradigm is reluctant to switch to the new paradigm, and often explains away errors with preposterous explanations, much as one tries to rationalize post-hypnotically.