Why do some say that humanity will become extinct?

Humans, all life on Earth, the Sun. All will eventually end, and just a matter of how much time.

The Earth's core is cooling and eventually, the iron core solidifies and the magnetic field of Earth ends. The solar winds slowly strip the Earth of atmosphere, and oceans evaporate. But that is billions of years away. (Polar auroras are lighting caused by solar winds)

Humanity ending?

Biological - A disease that wipes us out, that could come from Earth, or a meteor as alien. 95% of Native Americans were killed by disease brought in from Europe.

Nuclear war decimating the planet with radiation

A meteor strike that dust fills the atmosphere creating a winter that lasts for years that may have killed off dinosaurs.

Certainly, the Yellowstone super-volcano can erupt one day, maybe not killing off everyone, but the ash has the same effect of dropping temperatures and certainly killing many.

Alien invasion is not impossible.

Evolution to another form. Could also involve uploading into computers by consciousness giving up bodies.

Computers gaining consciousness or an an intelligence destroying humanity.

Earth orbit changing by a solar system change.

Gamma ray burst from a star or solar emission from the Sun.

Add- I did leave out climate change, pesticides and fertilizers, and the additions of chemicals in our diets reducing immunity, but wiping out all life is probably overstating. Could kill off half the humans probably. Climate change accelerates as the permafrost trapped gases are released, and polar ice melt flooding coasts and forcing us also to move towards cooler climates as hotter ones become uninhabitable. And our fish and seafood evaporate and animal feedstocks get killed off. It's certainly devastating, but I aimed at the "all human life" scenarios.

Many possible scenarios of anthropogenic extinction have been proposed, such as climate change, global nuclear annihilation, biological warfare and ecological collapse. Some scenarios center on emerging technologies, such as advanced artificial intelligence, biotechnology, or self-replicating nanobots.

Humans I hope are always looking for ways to save themselves, the best way is to find another earth and move their.

It's going to happen soon enough for you to worry about it. Unless some idiot is given the nuclear codes... Oh, wait!

The dinosaurs ruled the Earth for millions of years. But they became extinct, and scientists say they had to in order to usher in the era of mammals, since mammals would have been killed by the dinos. It's very possible that another species will replace mammals. 

On the other hand, my DNA analysis says that I am one of the millions who are directly descended from one woman in AFrica, about 10 thousand years ago. There were other humans, and other women, but this woman's children lived and thrived more than the others. So she became the "mother of us all". Millions and millions of humans could be killed off, but if a few survive, the earth could be repopulated. 

Because it will.

It could happen in any number of ways.  We could destroy ourselves with weapons.

Intelligent machines could decide to kill us all.

A large asteroid to slam into the Earth and kill us all.

And if nothing else, millions of years from now, our star will turn into a red giant and swallow the Earth.

a) Wrong forum. It's a science question.

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b) Eventually the sun will deplete its hydrogen to the point that it will start heating up. When that happens, the earth will get baked into a dry, waterless rock and every species down to the smallest microbe will become extinct. FACT.

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c) Unless mankind can figure out how to travel to another habitable solar system lightyears from here, it's bye-bye birdie, and everything everybody has ever done will become meaningless. Sleep well tonight with that thought. 

A.J. gave a fair listing. Except for random events over which humans have no control, the biggest threat at this time is that homo sapiens will continue to alter the planet's seas, soil, and air in a manner that will cause the Earth to shrug us off as just another failed species. 

Fear-mongering.

It probably will. The planet has been around for over 4 billion years. Humans only a few thousand. Most species die out eventually at some point, why not humans.