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

Indeed, we think that the human race is the world’s biggest problem and the cause of most of the suffering, but humans are far from being the world’s only problem. There are many other suffering factors on this horrible planet. The total extinction of all species and the end of all suffering on this planet is our moral aspiration. Please check the article Non-Speciesist Suffering, the answer to the question Why Nonhuman Animals Too and the post The Violence Even Activists Are Disregarding.

We disagree with the rather common notion that extinction is in itself morally wrong. We think it is a false argument based on an ethical misconception.
A species is a notion, a concept, not a sentient being. It can’t feel. It doesn’t experience. It can’t suffer. A species has no intrinsic value, no worth in itself irrespective of the individual members constructing it. A species is not itself a being with the ability to experience suffering or to have any kind of preference. Therefore a species is not a moral entity.
Individual sentient beings who are members of a species however, do feel and do experience and therefore are moral entities.
Morally, viewing individuals in species terms is false since experiences take place at the level of the individual only, not the group. The wrongness of hurting someone is not rooted in the belonging of that someone to a specific species. For the individual, it hurts just as much if s/he belongs to an endangered species or not.

Furthermore, as broadly explained in the article The Anthropocentric View of the Environmentalists viewing abstract terms such as eco-system, nature and in this case - species, as moral entities, is eco-fascism.
Not only that this view turns abstract terms, including of course the term species itself, into moral entities, it perceives these made-up entities as morally superior over actual moral entities. It almost makes them the only thing that matters. These abstract terms are the basic moral units, instead of an actual living, sentient individual. Individuals are completely expendable.
According to this view the “quantity” of animals and the variety of the species on the planet is what matters, not the quality of their lives. It is as if maintaining populations is the goal, not their living conditions and certainly not how each member feels.

Like in fascist ideologies, the continuity of the group is much more important than the well-being of its members. The system is much more important than the individuals forced into it.

However, it is the suffering of every sentient being that is meaningful and so “actions against the species” are meaningful because they cause suffering for its individual members, not because it hurts the species.

The only ethical relevancy of a species extinction is its impact on the individuals who gradually die out and individuals from other species who are affected by the extinction of that species.
As opposed to humans’ actual enormous ecological influence, the human race theoretical ecological "role" is supposed to be very minor (considering its original place in the food chain and what was supposed to be its impact on the environment, the human race should have been a marginal species in biosphere terms. Humans’ nutrition is not based on a specific species and vice versa, there is no other species that its nutrition is based on humans so ecologically speaking, the human race is not supposed to be important). Given that, and considering that its role in global suffering is probably greater than all the other species combined, there should be no moral dilemma about human extinction if you think that extinction is morally relevant in itself.

In principle the argument against extinction is philosophically false. In practice the argument against human extinction specifically, is inconsistent and speciesist.

If you have a problem with 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 dozens of species extinction per day. In fact, this period is referred to as an extinction wave, named the Holocene extinction, or the Sixth Extinction, starting from about 12,000 years ago, and attributed to the human race activity. If you are theoretically against the extinction of the human race, you are practically in favor of the extinction of at least 1,000 and up to about 50,000 species per year.

This rate is between 1,000 to 10,000 times the natural extinction rate, estimated (using the fossil record) at between 1 and 5 species per year.
The species you refuse to annihilate is the one causing all of these extinctions.

And the annual extinction rate is increasing still further. By 2100, according to current trends, about half 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.

According to the UN since 1950 half of the world’s forests were destroyed. Each year, a further 15 billion trees are cut down.

Since 1950 humans have managed to wipe out more than 90% of all large fishes, leading to the widely known estimation that by 2048 the oceans will be empty.

Roughly one-third of the world's coral reef systems have been destroyed or highly degraded. And all of the world's reefs are predicted to be lost by 2050 due to destructive, human-related activities.

In only a few decades, more than one-third of the planet's arable land has been lost due to erosion or pollution.
It’s not just animal based agriculture that is liable - the most common plant agriculture practices such as tilling, plowing, mono-culture, use of pesticides and fertilizers are major contributors too.
Also, other human activities such as urbanization, road paving, deforestation and global warming contribute to the arable land loss.

Opposing the extinction of the human species despite its responsibility for the extinction of so many nonhuman species, is specieist.
It is the same logic as in the case of animal consumption. Giving the abusers unlimited opportunity to change while they keep their abusive routine is considering them as more important than all of their victims.
And given the average animal consumption figures of each human, each is worth thousands of animals. Average American meat eaters are responsible for the life of suffering of about 55,000 animals within their lifetime, including about 10,000 crustaceans, 1,860 chickens, 950 fishes, 55 turkeys, 30 pigs and sheeps, 8 cows, and between 35,000 and 50,000 of non-directly consumed fishes and crustaceans who are either “by-catch” or animals captured and killed to feed the directly consumed animals. And of course that is without counting the chickens suffering in the egg industry and cows in the milk industry. Morally opposing to stopping humans, by all means necessary, including killing them, means they are worth more than the pain and suffering of all of these nonhumans.

Animal extinction was not one of our reasons to start the E.A.S movement. We don’t argue that the human race should be eradicated because it causes the extinction of other species, as we don’t think species are moral entities. We argue that the human race must be eradicated because it systematically hurts the species’ individuals.

But if you are against extinction, the best thing you can do about it is annihilate the human race. Annihilation of the human race is the only solution from that point of view too.