Why wouldn't common design fit what we observe? If I make 100 different animals out of similar dirt, would they not all show similarities at the subatomic level that could be confused as sharing common ancestry? Even if each one was created separately?
It's more complicated than that. When we look at evidence for common ancestry, we're really looking at
patterns of observations of things that should hold true if common ancestry were true.
Take phylogenetic tree construction as an example. A phylogenetic tree is a hierarchy of ancestral relationships predicated on shared ancestry. The tree implies two things: 1) that branched groups of organisms once evolved from a common gene pool; a common genome if you will. And 2), that the divergence between populations is primarily a result of hereditary descent with modification (i.e. mutations).
If I take a particular gene homologous to a bunch of species, I can construct a phylogenetic tree based on the individual genetic sequences for that gene. The results is a tree which shows a nested hierarchy of presumed ancestral descent of that particular gene. The nesting basically shows the ancestral relationships of the respective species groups.
Then if I take a second gene, I can do the same and generate another tree. If that second tree shows convergence with the first tree, then it reinforces those ancestral relationships.
Then I do that again with a third gene, or some other sequences of genetic code (i.e. ERV insertions) or morphological characteristics, or whatever. If I continue to converge on approximately the same tree, it reinforces the pattern that we would expect to observe if those species shared common ancestry.*
Now, if an intelligent creator was engineering organisms separately, they would not be operating under the same constraints (i.e. common ancestral genomes and hereditary descent). They could mix 'n match different genes or other genetic sequences willy nilly with no regard for any sort of pattern. So doing phylogenetic tree reconstruction under those circumstances, I would expect trees to diverge wildly.
This is why when creationists claim that such observed patterns are really evidence for common design, all they are really saying is that the creator was operating under constraints we would expect if organisms shared common ancestry via hereditary descent. In effect, the creator made life to have the appearance of evolution.
(* In practice things are admittedly a little fuzzier. For example, constructing gene phylogenies technically shows ancestral evolution of the specific gene which may not be completely in line with species divergence. As well, there are also mechanisms for horizontal gene transfer which can violate ancestral hierarchies. And of course like any statistical approach, there are going to be implicit assumptions and error margins associated with the output. All that said, we never do observe anything with respect to these reconstructions which would blatantly point to independent design.)
