Alfred Wegener was not able to provide a convincing explanation of how continents could move through the viscous Earth. Unlike air that moves around during to heating of ground by sun (and rotation of Earth) moving HUGE blocks of rocks was not understood.

Later when geologists realized that the Earth’s interior although solid actually behaves like a VERY VISCOUS FLUID did it become clear that the interior COULD MOVE at rates of a few inches per year.

Although continental drift was on the right track, Alfred Wegener lacked a MECHANISM by which the continents could move. He thought that continents 'plowed' through oceanic crust like a bulldozer - VERY wrong! Had he lived in a different time, he would have had better luck, because in the 1950's a scientist named Marie Tharp discovered the Mid-Oceanic ridge (this is literally the map that she drew BY HAND):

Mid-Oceanic ridge.

Then in the 1960s, people started to think that maybe new crust was being created at these mid-ocean ridges. In the late 1960s (after the Great Alaska Earthquake), scientists began to understand how oceanic crust becomes destroyed (in subduction zones, where it gets 'recycled'. This came together to ultimately take shape as the theory of plate tectonics.

So, although Wegener had the right idea, he couldn't explain HOW it had happened. It's only been for the past 60-70 years or so that Earth scientists have really started to understand how the different plates of the Earth's crust move around!

There is a thorough answer to this already on ScienceLine.

Essentially, Wegener's proposal ( the theory of continental drift ) was rejected because (i) established experts firmly believed in another theory (that the continents and oceans were fixed in position), and (ii) Wegener did not provide a reasonable mechanism which would enable continents to move in the manner he claimed.

Views on moving continents began to change in the 1950's as new measurements were made, such as geomagnetic patterns in the ocean floor and those providing evidence for sea floor spreading. Eventually, the ideas led to a new (and current) theory known as Plate Tectonics.

Side note - many do not distinguish between continental drift and plate tectonics. The first refers only to the motion of the continents, with no suitable associated mechanism to cause that drift. Plate tectonics is a theory which encompasses both the motion and mechanisms.

Another interesting point is that Wegener was not the first to propose that the continents had previously been joined as a single supercontinent; he even credited others who had similar ideas as early as 1848.

Other scientists did not believe Alfred Wegener's theory of continental drift because they did not see any way that continents could move through the oceanic crust and the mantle, nor did they see evidence that this had happened. They weren't aware of anything that could cause continents to move. What changed was the realization that it is not the continents themselves that move through the rest of the crust. Rather, entire tectonic plates with both continents and ocean crust on top of them move as whole units.

They didn't believe Wegener because his theory made no useful predictions that could be tested, and would eventually turn out to be wrong.

Although Wegener did predict continental drift, his theory for why the continents move made no sense and is indeed false. It wasn't until many decades later that oceanic ridges were discovered, indicating the existence of convection within the mantle, that a way that continents could move would be found. Thus, while Wegener was right about the existence of a phenomenon (i.e. continental drift), he was right for the wrong reasons, and the behavior of continents in where, how, and why they move, was completely different from what Wegener proposed.

It's a strange idea - that we live on plates on the surface of the Earth, and that these plates are slowly moving!

This wikipedia article has an awesome little movie that shows how one land mass broke up into today's continents, in the last 250 million years. To me, that's recent, because the earth is more than 10 times older than 250 million years - the earth is 4 billion years old. Some scientists think the earth was covered with water when life started, almost 4 billion years ago.

The wikipedia article says scientists didn't believe Wegener, because they didn't know of anything that could make plates move on earth's surface. This article is about Plate Techtonics, which is how we think the plates move.

Wegener was challenging a theory that many scientists at that time already believed. When a lot of people believe in something, whether it's right or wrong, changing their minds becomes difficult. This was one of the reasons that the scientists at the time did not believe him. Another reason was that some of his estimates did not match observations, and since these estimates were based on his theory, the mismatches made the theory seem less valid.

This is a standard practice in science: If estimates that come out of a theory do not match experimental observations, then either the theory is flawed and needs fixing or the theory is completely wrong (assuming that the experimental observations are valid). There are probably other reasons that would require some historical analysis, but the reasons above are two of the main ones.

It would be useful to read about both Wegener's theory and his opponents' theories.