The planet earth is not dying.
You may be right but consider this. Everything living is dying. Do you think planet earth will live forever? So then like you, it is dying.
But you are probably right the earth will continue to live long after humans are gone. In fact it will still be living when it finally meets it's maker, which is the sun will eat the earth eventually.
While we're on the subject of movies, consider 2003's
The Core. The story is that Earth's core has mysteriously stopped rotating, so the US government backs a plan to drill to the centre of the Earth and restart it – because without an active core, Earth loses its magnetic field and all life is threatened.
The Core is mostly nonsense and has been rightly derided by scientists. But not all of the science it features is junk. Some researchers really do think that Earth's magnetic field deflects ionising particles from the sun, which would otherwise wear away Earth's atmosphere. If they are right, then without a magnetic field our planet will lose its atmosphere too, and all life will die.
many of the mass extinctions in Earth's history were caused by life.
For instance, about 2.3 billion years ago lots of oxygen was released into the atmosphere by new forms of photosynthetic life. There had never before been free oxygen, so the microbes living on Earth could not cope with it, and a
massive extinction followed.
And no matter how green we go we might get wiped out by a meteor, blast of gamma rays, hit by a wandering star, volcano or nuclear war.
But eventually if none of this happens we will be eaten by an expanding sun.