What arguments are there for arguing that human reproduction (in modern times) is not pointless?
Since there are few reasons which make it irrational:
I have been hearing some of David Benatar's antinatalist arguments recently, so have been thinking about this. People readily dismiss his case, but don't in my experience then make a positive case, like you ask for.
There is a sneaky universalising that goes on, whereby suffering, pain etc are considered universal and objectively meaningful, but meaning and purpose aren't - that's inconsistent. It seems to be they are the same kind of thing - judgements or reactions for navigating the world.
The population in developed countries is generally dropping rapidly, except in immigrant communities. Female education, good birth and infant care, availability of contraception, look to give birth rates like Japan. However, climate change and resource use are overwhelmingly driven by those stabilising or declining developed world populations, so.
That draws attention to culture. We can impact our culture in many ways, as active citizens through participation, and through pursuasion abd influence etc etc. But, probably no cultural impact we can have is more impactful than that we have through having a family. Through that, we institute a mini-culture, with a particular capacity to spread. If say we focus a family on reducing climate & resource impact, that can help lead a change in the next generation. This is the most poweful impact most of us can have, if done well - or, badly..
You can't justify having children if you don't think you will be a good parent. Having sufficient resources, that may be more ambiguous & based on optimism, but realistic appraisal has to help.
I am deeply suspicious of the urge to have objective meanings. It's like approaching the world with your eyes closed, having already decided what to see. Given the idea of all meaning being 'subjective' (subjective like say, Indra's net!), what is good comes down to what we have the intelligence to argue for coherently, and the passion and fortitude to believe. And, if that makes us more adaptable and resilient, it will be more likely to survive, along with adherents.
Being human is challenging, full of pitfalls and pains. But we have the scope in each of our lives, to be among the happiest and most fulfilled animals. It is sad we are so damaging the natural world right at the moment we can truly appreciate it. If we have found happiness and fulfilment, and we truly think we can help others to, we should say yes to life, and pay forward the care and support we had as children, to the next generations. Who can continue the task of healing & understanding the world.
It would be very hard to argue that human reproduction is truly pointless. There are far too many "points" for it to lack any. So, either I am misunderstanding your question, you are ignorant of some of the most common "points" for doing things, or what you really mean to be asking is whether or not those objectives can be confirmed objectively, or somehow overcome certain oppositions.
Let's consider that there are many purposes for human reproduction. There's the religious argument which explains that we are here for a purpose and that reproduction is a part of that design. There's the biological argument which would explain that we are simply products of a process which seeks to spread our personal genetic material, not necessarily to ensure our species' or environment's survival. Then, there's the concept of pleasure, meaning that if nothing else, we each have some sort of innate drive to participate in acts which lead to human reproduction. These are just a sample of vast categories, each of which would likely provide lots of "points" to reproduction.
Therefore, to invalidate them, you would have to make equally valid points opposite them. These are much harder to make. You might attempt to present the survival of some subset of the environment as being desirable to survive, but once you exclude human reproduction, it seems that you've created some sort of slippery slope where you might have to figure out why a bunch of birds surviving without humans surviving is preferable to neither surviving, and if so, then which things are important and why, and then why should humans care more about that end than their own end. You might argue that there is no meaning, such as nihilism, but if there is no meaning, then why should we not at least have fun? I think that most people if they had no moral hangups at all would probably opt for optimal reproductive activities from pure impulse alone.
Overall, it seems to me that while people might hold different worldviews and there is sure to be one for everything, overall, you're going to find it much harder to show that human reproduction is pointless than to show that it is not pointless, and if you choose the former, it might end up being such a narrow proof that it only applies to a very limited set of people who would agree.
Nature works in this way, that people reproduce in pairs; they do not need an approval, sometimes by accident too! Making a philosophical inquiry on top of a sexual act, seems meaningless to me. It happens that the more you try, the less you may be successful, this thing has a dynamic of its own. Pointless or not, is out of our control, so even questioning about it, is arrogance at least.
X is not pointless? Do you believe things in general have purposes???