The strongest argument about Darwinian theory of evolution would be that progress trough random mutations is statistically improbable, given the huge size of the DNA. And the natural selection is not a helper to increase probability. It decreases it instead.
Darwinists from the time of Darwin think that they explained away the problem of probability law by pointing to the HUGE (this is the "scientific" term they use) number of individual organisms independently mutating all the time. Surely, some mutations will take them to the higher evolutionary level.
No, it is not. HUGE is not a number in the Mathematics. When proper number of mutations possible to occur over the time Earth exists is estimated, it looks quadrillion times lower than the number needed to win the Darwin lottery even once. DNA happen to be HUGER
This argument is known as the "irreducible complexity".
But there is fair amount of math involved to demonstrate this problem.
The good proxy argument would be that over the last 150 years having absolutely no opposition in biology Darwinism did not come up with a single test to prove its theory.
All they had proved is that species did evolved. But so are computers.
Slick Apple Laptop evolved out of the first clumsy desktops made in the garage.
But it is far from proving that Apple Laptop got where it is today through the random minor changes (bugs and damages) to the old desktop. Quiet the opposite - there was an intelligent designer, who drove the changes (Steve Jobs?).
There is also abundance of the very solid observations Darwinists keep bringing over as proof of their theory. Some of them are about humans breeding new species by INTELLIGENT breeders. They love to illustrate possibility demonstrating how INTELLIGENT bank robber is opening the vault number by number.
They are so blind that those arguments show that INTELLIGENT design (aiming at the specific goal many steps ahead) might work. Not the blind forces of nature.
They have absolutely nothing to demonstrate that random mutations and blind natural selection (no planning for the future is allowed) might move species up the evolutionary ladder.
While Darwinists are cluelessly wondering in the biological wilderness genetic engineers are fast approaching the point at which humans will be able to design stable species living in harmony with the environment. That would be duplication of the work done by somebody else who genetically engineered us.