Hancock says that due to weathering patterns and other evidence, it is likely the Sphinx and or Great Pyramids are thousands of years older than the currently accepted dating. What are people like him missing or ignoring that point to them being wrong?
First, the science of the "weathering" hypothesis is decidedly bad science, and has been thoroughly debunked in so many papers and publications that it is impossible to list them here. See here. And see the comments for a great case study on how pseudo-scientific evangelism can infect people.
Second, not a single shred of evidence supports a much earlier date for a civilization in this region, much less monument-builders. Not a single inscription, burnt bit of charcoal, broken sherd of pottery, fossilized feces—nothing. Magical civilizations which can construct monumental stone structures do not vanish without a trace without leaving a single shred of physical evidence. That's just not how archaeology works. If the Sphinx was constructed millennia before its context suggests, we can expect the site to have other evidence conforming to that date. Even if the site had been scoured clean to bedrock by Khafre's or Khufu's work crews (as Schoch hilariously suggested back in 1992), the evidence of that scouring would be plainly detectable in the stratigraphy.
Third, the context of the greater site, including the pyramids and the causeway, strongly suggest that the Sphinx belongs with those other buildings in a logical progression of the site's layout. See Lehner's many explanations of this. The origin of this conspiracy theory is Schoch in 1992, so this is now nearly 30 years old, but the momentum for it goes back to the 1950s, to fantastic imaginations brought forth by dreams of aliens and the supernatural in popular culture.