I will answer this question first. I would a say that there is some pretty strong evidence that they did share a common ancestor. However, I am not really convinced of it. There are aspects of humankind that are hard to explain with evolutionary theory - such as the will, morality, consciousness, etc. There is something special about humans that sets us apart from the animals and make us special in God's sight. So at this point I would say no, I am not convinced that humans shared a common ancestor with apes.
Let me see if I can clarify my thoughts here. When we observe DNA similarity across a wide range of organisms it is compatible with both common descent and with ID. We agree on that part.
The prediction part is where the confusion comes in. Lets say we have two organisms that we are unsure if they are related or not. Common descent would predict that in order for these organisms to be related by descent they must have similar DNA sequences. In fact, the sequences should be different such that it can be explained by a known process. As a simple example, consider the hypothetical organisms below (the letters represent genes)
A B C D E F G H I J K L - Organism 1
A B F E D C G H I J K L - Organism 2
We can see that these organisms differ by an inversion of the sequence C D E F, which is a known genetic phenomena and has been observed and studied in several model organisms.
If the sequences were more like this:
A B C D E F G H I J K L - organism 1
B D L J A C F H I K E G - organism 2
We could conclude that these organisms are not related because there is no mechanism that can explain these genetic changes. My primary area of study / interest is in plants, and this is exactly what is going on in plant systematics right now. With the data that is coming in from mDNA studies there is a major reshuffling as scientists are concluding that plants that were formerly thought to be related cannot actually be related and instead are related to other genera. I don't believe things are moving past the family level, but genera are certainly being reorganized.
So, that is how the predictive aspect of common descent works.
ID or more specifically special creation does not have that predictive aspect, IMO. What is to require the designer to build organisms in this type of predictable manner. For example, what would preclude the designer from building these organisms in the following way?
A B C D E F G H I J K L - house mouse
B D L J A C F H I K E G - white rat
Nothing would prevent the designer from organizing them in this way. So that means there is no ability to falsify any hypothesis about ancestry. Actually the human / chimp issue is a good example of this. Human chromosome 2 is thought to be a result of a fusion event between two chimp chromosomes. The correlation is stunning. Here is a bit about it http://www.evolution...hromosome_2.htm .
Common descent explains and predicts this (as I explained above). Fusion events are observed and studied. There is even a human living today that has undergone a similar fusion http://genetics.thet...al_news/news124
How does ID / special creation predict this situation. Lets forget for a second that we are talking about the human / chimp issue. What could you conclude about the following senario:
A B C D E F G H I J K - organism 1 (2 separate chromosomes)
A B C D E F G H I J K - organism 2 (1 fused chromosome)
You could easily conclude that organism 1 underwent a fusion event which gave rise to organism 2 (remember, fusions are observed - not just made up).
But now make it about the human / chimp issue and suddenly the rules change. Now an Intelligent designer could have designed it that way and it just looks like a fusion event. Do you see where I am coming from now? There is no predictive power in that. There is nothing to preclude a designer from designing in any fashion he chooses and there is no requirement that it be consistent.
I hope that clears up what I mean by predictability favors common descent rather than special creation in this case. And note that I am restricting this statement to the topic at hand only - I am not broadly painting this on every aspect of this debate.
That said, I am seriously puzzled by the evidence for human evolution, but I just am not convinced. I guess this is one area I do hold onto the in the Biblical account. It is hard to get around the fact that God made man in His image in order to have a relationship with Him. I have been unable to reconcile that idea with the idea of humans and chimps sharing a common ancestor.
Let me restate this in a way that I believe makes more sense and sheds a different light on the situation. Common decent sets more specific constraints on what it predicts will happen in reality. Special creation allows for either completely different genomes for creatures that appear similar or very similar genomes, therefore not predicting much specifically in this realm.
The specific parameters of common decent makes it seem more scientifically testable, but this is the only advantage in theory. Creationists can easily take a stance one way or another when predicting data similarity within the genome, for example I predict that organisms that appear similar in structure require similar genes to produce such similarity. Predictability of common decent is an illusion because when chimpanzee and human genomes were compared and found to be radically different than predicted, the expectation was adjusted to accommodate common decent. Not only that, the imagined evolutionary split between chimpanzees and humans was pushed back millions of years, since it would have taken many more generations than previously thought to explain all the deletions, insertions, etc etc etc that we observed when comparing the genome. Rather than predicting anything, common decent accommodated anything, just as you stated for special creation. What I object to is special pleading for evolutionary thinking, assuming it is somehow a better presupposition to further scientific inquiry. Clearly it has no specific advantage.
Lets not confuse things though, I understand that some organisms share common ancestry. I share common ancestry with my brother, my mom and dad, my grandma etc. Plants share common ancestry with other plants, etc. I believe that if we took the time to develop a human genome and a chimpanzee genome without gaps, without using the human genome as a backbone for the chimpanzee genome, common ancestry assumptions would have to accommodate even more radical differences.