What specific evidence proves we have the same ancestor?
Remember to leave out those pesky terms "theorize" and "believe".
Before I present the evidence, I'm going to point out that your request to leave out those two words betrays a failure to understand one of the key points of science: that we can never know anything for certain, beyond any possibility of doubt. Certainty beyond the possibility of doubt is the arena of dogma, not science. In fact, I submit that this is precisely why religious doctrine strays further from the evidence than science: it is believed with such arbitrary certainty that checking the facts is never done.
When you ask "what evidence shows we have the same ancestor?" it's also important to include the context of the question. If one accepts the model of evolution for the divergence of species, then the question means, "What evidence shows that humans and chimpanzees have the same ancestor, as opposed to humans being descended from chimps, or humans being off the primate tree altogether?" If not, then the question means, "What evidence shows that humans and chimpanzees have the same ancestor, as opposed to humans and chimps being separate creations?"
It's better to present evidence for evolution in general rather than in specific; that is, evolution is simply the only non-nonsensical explanation for the temporal divergence in the fossil record generally. The evidence that humans and chimps are not separate creations is that the emergence of the two species in the past is separated by about twenty million years.
Pan troglodytes is about twenty million years old, while
Homo sapiens emerged only 100,000 to 200,000 years ago. And of course, similar observations may be made about other species of life. So unless we have a creation that keeps happening, with new species being created all the time over hundreds of millions of years (which differs sharply from the Genesis account), creation is a model not consistent with the observed facts.
For this reason, I'm going to present answers that assume evolution, and explain why humans and chimpanzees probably share a common ancestor rather than one being descended from the other or hominids representing a completely distinct, non-primate line of animal life.
Evidence for humans and apes sharing a common ancestry is partly genetic and partly from the fossil record. You can find both here:
The Evolution Evidence Page.
Details on the genetic similarities among humans, chimpanzees, gorillas, and orangutans can be found from that link by clicking on the "chromosomal evidence for common ancestry of apes and humans" on the frames on the left. Roughly stated, we have strong congruence of many of the human chromosomes, in one, two, or all three of the ape species, and greater genetic similarity than we find in other animals. (Which, given the phenotypic similarity, is what we should expect.)
Talk.origins, despite your ad-hom dismissal of that source, actually has a very good rundown on the fossil evidence for ancestral hominid species.
Fossil Hominids: the evidence for human evolution. Here is a timeline on the process:
Hominid Species. The
Australopithecus genus is where the two lines appear to have branched, well before the
Homo genus emerged. Note the characteristics listed in the key: small or large brains, small or large teeth, quadrupedalism or bipedalism.
Hominid Species The species
Sahelanthropus tchadensis is the best candidate so far.