The argument, in short, goes like this: Humans have 23 pairs of chromosomes, and all the other great apes have 24. Before we look into the details, we can make a prediction: If evolution is accurate, we should find where one pair fused with another, in the human genome. If we can't find such a thing, a good chunk of our theory could be in trouble.
It happens that we did find evidence of a fused pair of chromosomes!
Now, this does not, by itself, prove evolution is true. What this shows us, at least, is that evolutionary thinking is good for conducting science.
At any rate, it proves that the number of chromosomes can change, over time, in a lineage... without an intelligent designer needed to do it. If you still wish to invoke a designer, you have to show us evidence of its intervention.