There is a difference between microevolution and macroevolution. Microevolution is observable and supported by evidence, while macroevolution has no direct evidence for it, but has direct evidence against it.

Microevolution is small changes within a species, such as the beaks on the birds Darwin is famous for. Macroevolution is an extrapolation that these minor changes could add up to create new species. An extrapolation which, despite various experiments, has only had evidence appear against it, rather than in favor of it. The biggest argument against macroevolution is irreducible complexity. [1]

"If it could be demonstrated that any complex organ existed which could not possibly have been formed by numerous, successive, slight modifications, my theory would absolutely break down..." [2]

While Darwin followed this up with "But I can find out no such case," he lacked biochemistry and microbiology. Experts in these fields have found numerous irreducibly complex systems that cannot be explained by Darwinian evolution.

The most commonly used example is a five-part mousetrap. You cannot take away one of its peices without breaking is functionality. Similarly, you cannot remove a part of certain systems (i.e. a flagellum or cillia) without breaking its functionality. [3]

The most common response to this is, "Someone could build a mousetrap out of three or four parts." However, that is not the point. The point is that you cannot go from a four-part mousetrap to a five-part mousetrap without needing to take it apart and break functionality along the way. Evolution requires an unobtrusive addition of additional parts.

DNA mutations are common, but they are almost always neutral or harmful. Beneficial mutations are exceedingly rare, so much so that when testing 1.2 billion genes, not a single beneficial mutation was found. [4]

This demonstrates that the likelihood of finding a beneficial mutation to a DNA sequence is so low that it is effectively impossible. This is because DNA is a highly complex system, and even a single base pair change can have a significant impact on the function of the gene.

Beneficial DNA mutations are already rare, mutations of proteins are even rarer. And the likelihood of even the simplest of proteins randomly generating a beneficial adaptaion is, for all intents and purposes, impossible.

The hard numbers are estimated as follows: The odds of a truly beneficial mutation to a protein taking place at any time in any organism's life throughout the history of life on earth is 1 in 10^33. That is, for all intents and purposes, impossible.[5]

The Cambrian Explosion shows rapid appearance of complex life forms

This sudden appearance of diverse life forms is difficult to explain through gradual evolution alone.