I agree that the human race is the world’s biggest problem and the cause of most of the suffering but I am against extinction

This argument is not consistent and it is speciesist.
If you have a problem with animal extinction then it is actually supposed to be another reason to annihilate the human race, because it is the human race who is responsible for between 50 to 150 extinctions per day.
If you are against the extinction of the human race, you are in favor of the extinction of about 100 species per day which is more than 35,000 species per year.

This rate is at least 10,000 times greater than the 'background' or natural rate of species extinction, estimated (using the fossil record) at only 2.5 species per year. Mankind is responsible for all this.
The annual extinction rate is increasing still further. Over the next few decades, earth is on course to an extinction of 50,000 species per year. By 2100, according to current trends, fully two-thirds of all species will go extinct.

One in 4 amphibians is an endangered species, so is one in 4 mammals, one in 8 birds, one in two crustaceans, one of every 5 fish species and one of every 5 reptiles - all are endangered species.

And that is not all:
More than 50% of the world's wetlands have been drained.

Since 1950, some 7.5 billion acres of forest - nearly half - have been lost.
Each year, a further 40 million acres of forest are destroyed.

50% - 80% of mangrove ecosystems have been destroyed.

Roughly one-third of the world's coral reef systems have been destroyed or highly degraded.

One-fourth of the planet's topsoil has been lost.

Nearly 2 billion hectares of crop and grazing land are suffering from moderate to severe soil degradation.

Animal extinction is not one of our reasons to raise the O.O.S movement, but if you are against extinction, the best thing you can do about it is extinct the human race.
Annihilation of the human race is the only solution from that point of view too.

It is the same with eating meat. An American meat eater is responsible for the abuse and killing of nearly 3,400 animals within his/her lifetime, including 2,460 chickens, 800 fish, 96 turkeys, 32 pigs and sheep, and 12 calves. Refusing to kill him means he is worth the pain and the suffering of all of them. Simple math, if he stays alive – all these animals won’t.

Most humans have a problem with extiniction for selfish reasons. They are sad because they cannot watch a certain species anymore.
The problem with extinction is that individuals suffer before they die and that extinction of one species affects individuals from other species. For most humans biodiversity's role is to entertain and interest them.
Most humans are not aware of the single significance of extinction which is, as said before, the effect over individuals from another species. Besides that, there is no rational reason to mourn the death of the last individual from an endangered species more than the death of any chicken in the meat industry. And we shouldn’t be mourning when a chicken dies because every single moment in the life of a chicken in the meat industry is a nightmare. We should be glad for their death, not sad. It ends their misery.
Yes this is the world we live in. Death is the salvation for most of the living creatures.