It is the evolution of our knowledge
As we know more we can change how we group or classify animals
It is done through a scientific method
Humans ARE animals
Human are Apes
There's that pesky scientific classification for you
And no, you do not know for a fact that DNA can't prove human ancestry with other animals because it does (or at least prove it as close as anything can be proved).
"Analysis of DNA sequences now plays a key role in evolutionary biology research. If Darwin were to come back today, I think he would be absolutely delighted with molecular evolutionary genetics, for three reasons. First, it solved one of the greatest problems for his theory of evolution by natural selection. Second, it gives us a tool that can be used to investigate many of the questions he found the most fascinating. And third, DNA data confirm Darwin's grand view of evolution."
Darwin would have loved DNA: celebrating Darwin 200
So when we say Humans are related to chimpanzees or gorillas or bananas it means if you go back in time far enough, we have a common ancestor.
Theists will often ask if humans evolved from apes, why are there still apes. But we didn't evolve from the apes you see today - we had a common ancestor species who split into 2 or more species.