I'm pretty sure species went extinct before any trace of humans existed on this planet.

As for the environment ... um who cares? Setting aside the fact that the impact that humans have on the environment is negligible, what value will the earth have to anyone or anything if humans are extinct? The environment will be destroyed eventually as a result of the sun burning up all of its hydrogen. The only thing that could possibly save the planet would be humans through some elaborate process of moving the whole planet somewhere else (never even heard of that being done even in sci-fi ). So yeah this planet is doomed in the long run even if all humans were wiped out tomorrow.

Our impact on the environment is far from negigible. Thousands upon thousands of species are extinct as a direct result of human activity, not natural causes. People die eventually too, doesn't mean we should murder them cos they're going to die anyway.

Ultimately, life on earth would benefit from our elimination.

I am not seeing what the benefit would be. Species always die. Humans are the only chance animals have to survive long term. Without Humanity life is doomed no matter what. With us life has atleast a theoretical chance to survive.

The benefit to them would be that thousands of species that we'll destroy in the next few centuries could survive. All lifeforms are doomed eventually, we can't save them or ourselves in the end. 

Just one. But you can name off more diseases if you want.  

Cancer is just caused by so many things now it is hitting people from young to old ages and it is so sad.  That is why I chose cancer.  Nobody is safe from it and it is becoming more common it seems.

So this is to save the species we will kill in the future before they inevitably get killed by nature. I see how this would benefit them but not life in general. 

In 500 Million years its definetly lights out for life on this planet. The Sun gets gradually hotter, over time a natural runaway greenhouse effect will transform Earth to Venus. 

While Humans will also die sooner or later. Life could survive way longer than Earth existed up until now. Blocking the Sunlight will prolong the time the biosphere has left substantially, not to mention deflecting Asteroids/Meteorites or preserving DNA to repopulate after mayor catastrophes.

Pulling earth away from Sun over Millenia is doable too. 

Recreating biospheres on former dead rocks too. 

Even if Humans don't get to the point its the only possible way for life in the solarsystem to survive. We have Multicellular life for 500 Millionyears I think its worth to not kill 7 Billion Humans in order to save several Billion animals for a couple of Million years before the next big rock inevitably hits.

I believe my life and the life of my family is more worth than the life of animals. Atleast for me, so I really don't think killing all humans for some animals I don't even know is worth it. And that its better for life in general I highly doubt that. All that would happen is instead of 1000 Billion Humans that get born its 1000 Billion Sharks, Whales, Penguins, Crocodiles, Apes, Rhinos, Elephants all those Species lived for ages, long before us. Where is the fairness in them getting to live even longer just because ? And they atleast get the chance to have their DNA preserved and maybe to be repopulated again somewhere if they infact die.

I'm going to go with cancer as well. Not only am I even more afraid of cancer than any other illness, but my aunt is currently fighting lymphoma. It's silly to wish for something like for a magical end to cancer, but that's the one I'd pick if I couldn't be more broad about it.

While on the topic. I read that a new form of human DNA was discovered that's is more than a double helix. It is only found in cancer cells. Which means if we can find a way to target that DNA we can kill all cancer cells. We may not be far from a scientific solution. Hopefully we will soon see a world that fears cancer no more than the common cold.

I'm going to go with cancer as well. Not only am I even more afraid of cancer than any other illness, but my aunt is currently fighting lymphoma. It's silly to wish for something like for a magical end to cancer, but that's the one I'd pick if I couldn't be more broad about it.

While on the topic. I read that a new form of human DNA was discovered that's is more than a double helix. It is only found in cancer cells. Which means if we can find a way to target that DNA we can kill all cancer cells. We may not be far from a scientific solution. Hopefully we will soon see a world that fears cancer no more than the common cold.

This might take a while (decades atleast). Cancercells can have various mutations and its not a single disease its just natural cell degredation causing massive problems and messing up other working cells. And it can have alot of different faces if you will. 

  Cancer will be the thing that if we fully control it we will be practically immortal since we found a way to not only destroy the broken cells but to refresh the DNA in all Cells and fix it.