As someone who understands, if not necessarily openly espouses, anti-natalist ideology, I can give a bit of elucidation from my perspective of the philosophy of utilitarianism, which I am happy to debate. It would be nice to be proven wrong here.

It comes down, in my opinion and understanding, to the following argument:

1. an entity is inherently unable to consent to its own creation. [A postulate]
2. suffering has a net-negative effect on the (perceived or actual) value of existence [precept of utilitarianism]
3. suffering knowingly enacted against any entity which cannot give informed consent is eqquivalent to the suffering of an entity which is actively not consenting [by which argument paedophilia is a crime]
4. The potential suffering inherent in life is foreseeable, as is the potential of a human life to harm the lives of others. [The basis of the concept of negligence]
5. An entity that is not created does not harm or cause others to suffer, nor does it experience harm or suffering [postulate]

From propositions 1 through 5:

5. You are personally, morally responsible for the life which you create, both its actions and its experiences, as all of its experiences and actions are exclusively contingent on the act of its creation. It is from this moral duty that parental responsibility derives.
6. there is a foreseeable possibility that the entity being created could endure enough suffering (or be the cause of same) to make the value of their life net-negative

From propositions 5 and 6, and the various observations one might make of the world (from climate change, to the renewed rise of fascism and the far-right, and a myriad of other "natural shocks which flesh is heir to"), they suggest:

7. On cost-benefit analysis, the expected value of a new life which I might create is net-negative.

From which:

8. it would be irresponsible (read: negligent) to procreate.

That is the basis. If you can prove each of those propositions, then from a utilitarian perspective, I think anti-natalism follows. I am personally convinced up to proposition 6, and I am personally waiting until I no longer feel that 7 has a chance of being valid before I have children. There are plenty of ways you can argue against the propositions, but as they stand, there is no indication of a moral duty to end already-extant life or to engage in mass-sterilisation of animals. There are certainly people who try to come at it from a nihilistic perspective, and it's MUCH easier to argue pretty much anything from nihilism than from utilitarianism, but I, being primarily utilitarian, hold with the above.

I also think that the person saying "anti-natalists think children are awful to be around" is presenting a ridiculous strawman. I'm a public school teacher, and I love being around kids. The wonder with which they view the cosmos is forever inspiring to me, but many of my students have experienced truly awful things. I believe my moral duty involves doing everything I can to minimize the suffering of entities that exist. I think that, once a child has been created, you now have a moral duty to make that child's life as free from suffering and as fulfilling and rich as possible (without imposing suffering on others, of course)