Let's check his assumption.
Humans have about 30,000 genes. Chimps have about the same.
Depending how you figure it, Humans and chimps are 92% to 97% similar to humans genetically. Let's say 90% to be conservative. So about 3,000 genes different. Divide by half, (because both humans and chimps have been evolving, and that difference is ours plus theirs) and we get 1,500 genes.
Every human has a few to a few dozen mutations that were not present in either parent. We know this has been true from the beginning because of human genetic variation. If we started from two individuals, they could have had at most, four alleles for each gene locus. Yet there are dozens of alleles for most human gene loci. The rest appeared by mutation. That means perhaps 150,000 mutations in that time. (being extremely conservative). From this, you can see that a few million years wouldn't be too little to produce observed differences.
But let's try it another way. Assume 20 years generation time (again, conservative). That would mean 50,000 generations in a million years. The time of divergence was earlier than that, but we'll use a million to be conservative. Suppose a population of 10,000 hominins. A very conservative estimate would be 20,000 mutations per generation, or about a billion mutations over that time.
Let's say only 1% of them were favorable, and that all the differences between humans and chimps must be favorable for each. That means 10,000,000 favorable mutations.
Well over the number needed to account for the observed variation. There is a very good reason why most scientists who are Christian do not agree with that book. There is an organization of Christians in the sciences; this is their statement of faith:
We accept the divine inspiration, trustworthiness and authority of the Bible in matters of faith and conduct.
We confess the Triune God affirmed in the Nicene and Apostles' creeds, which we accept as brief, faithful statements of Christian doctrine based upon Scripture.
We believe that in creating and preserving the universe God has endowed it with contingent order and intelligibility, the basis of scientific investigation.
We recognize our responsibility, as stewards of God's creation, to use science and technology for the good of humanity and the whole world.
It is mostly composed of Christians in the sciences, but you don't have to be a scientist to join. You do, however, have to agree with their statement of faith. The American Scientific Affiliation might be a way for you to see how Christians in the sciences see creation. If you agree with their statement of faith, why not take a look?
http://network.asa3.org/