i) Why are chimps and humans so alike? The evolutionary explanation is that they share a last common ancestor.
Were it not for theological reservations, that might seem like a plausible, straightforward explanation. At the same time, evolutionary explanations can be deceptively easy and vacuous. Take a comparison: why are different conifer species so alike? Well, I suppose a Darwinian could posit common ancestry, but the more direct explanation, the reason with the most explanatory power, isn't common ancestry but adaptation (or design) to a common environment. Conifers are alike because they reflect the same problem-solving strategy for survival in higher latitudes. To attribute this to common ancestry would be a "science-stopper."
ii) From a Christian perspective, what's the alternative explanation for the similarity between man and chimp? I've already offered a general explanation:
Now I'd like to suggest a more specific (but related) explanation. Let's take a comparison. Instead of asking, why did God make men and chimps so alike, let us ask why God make twins so alike?
Twins are strikingly alike in some basic ways. This begins with their fundamental genetic makeup. In addition, they have the same environment. Same formative experience. They are raised by the same parents at the same time. They live in the same time and place. Attend the same schools. Because parents can't tell them apart, they treat each twin the same way. So twins have the same nature and nurture.
Sometimes the affinity goes deeper. A friend of mine was telling me how he and his twin brother are synchronized to wake up at the same time. If his brother's work schedule changes, they both wake up at that new time. Not based on an alarm clock, but some internal clock they share in common.
Yet despite how much twins have in common, they often have very different personalities. (BTW, this is easier to account for on dualism.) And it's because twins are so similar in others respects that this makes their dissimilarities so striking. Their similarities supply the contrasting background against which we can more clearly observe the dissimilarities.
By the same token, what's more striking about chimps and humans is how radically different we are despite how much we have in common. And suppose God makes some creatures alike to highlight how unalike they can still be in spite of their extensive commonalities? We expect unlike things to be unalike. What's more profound is how like things can be unalike. That illustrates the wisdom of God, by creating diversity within very narrow parameters. It's the commonalities that make the variations stand out.