The fall of man and the rise of apes is the foundation of entire franchise in it's original form. They just started the remakes off at a different chapter than the Heston movies. I do wonder if they'll ever carry this one through to circle back around to where those started though.
Yeah, but as you said before--in those movies the story was almost always written for you to cheer for the humans, except 2-3, which were not nearly as popular and even then it was a mix. The first movie was brilliant though because the entire time you were there saying "no you stupid monkey, mankind is more powerful than you can possibly imagine!" The entire film you reveled in the achievements of mankind and how these stupid apes couldn't even fathom how advanced humans were. Even Taylor himself talked down to them, and regularly seemed frustrated with how primitive they were. The final scene, with the little doll which could talk, or the paper airplane midway through the film while he's trying to explain how humans can fly and go into space, those things were meant to show that even our children's toys were more imaginative and advanced then all of Ape society. The entire film was "humans fuck yeah"--teasing how even a small group of humans with out technology, or even ONE man (Taylor) who knew our technology could overcome the apes.
Which is what made the ending so spectacular. The Movie spend 90 minutes jerking the audience off to humanities achievements, and how magical our technology is, and how advanced we are...then it shows we blew ourselves up with it. The very thing we believed made us better than them, is what destroyed us. But the whole first section of the film kept you strictly on the side of humanity, and was clever about keeping you proud of our advanced society and technology. Again, right up until that last moment, when the movie slapped you and forced you to think about what Doctor Zaius was saying, and the fact that Zaius KNEW the truth, and what he was saying wasn't the idiotic ramblings of an ignorant ape--but the very wise misgivings of someone that had seen what human power could do, and knew to survive he had to avoid it. The apes knew not to eat from the tree of knowledge because they knew what happened when we did. (Which is why Zaius always shit on the scientist apes.)
But long and short, that's why the original movie was brilliant--it never really asked you to sympathize outside of humanity. It, in fact, asked you implicitly to be proud of humanity and tell those damn dirty apes who was fucking boss.