I generally have a problem with best-fit theories being accepted on the level of something like the theory of relativity. (which has been proven out with data) Here are legit complaints:
1) DNA, genes, and other markers such as this degrade too quickly in most cases and we are unable to actually confirm anything past say 30k years. So we know our own family tree up to that point, and know exactly who is related through that material to that point. Past that point...
2) Everything past the 30k mark is speculative. Things look like this or that so they are classified together, etc. It's barely science and mostly educated guessing. That includes taxonomic guessing as well. That means we can say chimps are 98% like us because of modern DNA, but have no idea in an actual sense if we were once directly related or that isn't just some freak coincidence. We share similar DNA with a lot of creatures such as various plants, cats, dogs, etc. We are literally biologically similar to everything else on the planet in some way, but whether there is a lineage or not is questionable because it is possible that similar "evolution" occurred in two places at once. If it did, then we don't know it and lack the ability to say. If it does occur like this, then our taxonomic understanding would be inaccurate.
I'm mostly middle-of-the-road with the concept, and I accept what we can prove through DNA and reject the best-fit information -- at least until we can prove it.