There is only one reason to deny that humans are apes, that reason is to remove the guilt of taking lives for no reason. In other words, it makes us nothing more than automatons incapable of compassion, love, or reason.
The psychological term is psychopath, not all psychopaths are violent but they are all incapable of feeling guilt. The most common behavior in psychopaths is indifference, the disconnect of not being animals allows them to ignore suffering in everyone, including their own species.
Animals have been culled by natural selection to care not only for their own, but for other species, sadly that includes humans. It is not uncommon for other animals to defend us when there is no instinctual drive to do otherwise.
The most well known cases involve domesticated species, though there are many examples of feral animals also coming to our aid, in spite of our habit of harming them for no valid reason. Our behavior stems from the disconnect we created by denying the obvious, we are a species of ape, mammals, animals, life.
Taxonomy classified us as apes centuries ago, one of those rare things we got right. The reason for the origin classification is our skeletal structure, later this was reinforced by our organs and brains, then confirmed by genetics.
To date, taxonomy has had about 20% of their classifications wrong, considering how long ago we started it that is a pretty good record. To deny we are apes today is the same as denying that roses are plants.
The lie of us not being apes spreads by the scam artists trying to say ape is a species, often saying "go to the zoo and see apes." But ape is a huge family, huge because we started burying our dead long before humans even existed.
A buried corpse has a higher chance of fossilization and takes a lot longer to decay. So we have well preserved skeletons of many ape species that are now extinct, and since 99% of all life on Earth has gone extinct since it's appearance, that's a pretty big portion of our lineage preserved.
Human lineage, down to the chimpanzee ancestor, is one of the most complete lineages, due to our desire in trying to prove the notion wrong. Ultimately, because of doubting the connection we actually proved it, a great example of how and why science works.
So to deny that we are apes is simply arrogance, the notion of being "special" or separate from the world. It is a dangerous lie that promotes psychotic behaviors and empowers abusers, killers, rapists, and other horrible people.
This is why we focus on those who deny science, we must protect our future and our sanity.