Why was the initial theory of plate tectonics so controversial?
One of the key aspects of plate tectonics is continental drift.

The person who came up up with the theory of continental drift was Alfred Wegener. He published his theory in 1912.

One of the issues with the theory that geologists at the time had, was that Wegener was not a geologist, but a meteorologist. He was publishing a theory that wasn't associated with his field of science. The other issue the geologists had was based on the commonly held opinion:

that the oceanic crust was too firm for the continents to "simply plough through".

When he published his theory, Wegener did not propose a means by which the different land masses could break away from each other.

Initially, some geologists could only conceive the idea that ocean waves might be responsible for breaking up land masses, but they couldn't reconcile the fact that the lack of sediments and the clean breaks in land masses would not support Wegener's theory. Without knowing about plate tectonics the theory of continental drift was difficult to support.

Another reason why Wegener's idea was not initially accepted was because of the way he proposed that continents used to fit together. This was because of the assumption most people had was that the continents split along the lines of coast lines and not the 200 m isobath proposed by Wegener.

Wegener came up with the idea of continental drift by noticing that all the major land masses appeared to fit together like a jigsaw puzzle.

It wasn't until the early 1950s when data from paleomagnetic studies of India showed that India had once been in the southern hemisphere that data started to support Wegener's theory. Also, it wasn't until the 1960s that sea floor spreading data was available to support the theory.