Can someone address this critique?

"Not being reborn is the goal" , that is the precise reason why we need to practise loving-kindness. Committing actions that sow the seeds of karma will cause you to be born again , it is the natural law of cause and effects. Only when one has given up all desire for the world, when one is enlightened , do the seeds of karma stop being ceated. Committing bad deeds leads to rebirth in lower realms of suffering. Buddhism is not nihilism , it is the complete opposite of nihilism. Buddha said that things to exist , but they are empty of "inherent existence". That means they are always changing as they are conditioned. Even the smallest particles inside any given object are changing with time. This is what he meant by emptiness. Infact he said that those who say that nothing exists are infact having "wrong view"

Ending suffering is the goal. Not being reborn is a result of reaching that state. Benevolent acts are conducive to reaching that goal. Hateful or cruel acts will take you away from that goal.

Buddhism does not advocate ceasing the will to live. It advocates reaching the highest bliss that is Nirvana. It also advocates happiness in the present life through living a virtuous life. See this answer and this answer.

Buddhism teaches neither annihilationism nor nihilism. See this question.

Should a Buddhist have children is addressed in this question.

Buddhism encourages the social and economic progress of humanity. See this answer, this answer and this answer.

The goal is the ending of suffering.

All sentient beings are suffering according to the first noble truth.

You want to avoid suffering and other beings want to avoid suffering.

So, why not avoid increasing the suffering of other beings, and if possible help other beings reduce their suffering?

So, find ways to reduce your suffering and reduce the sufferings of other beings too.

Bhikkhu Bodhi wrote in "The Balanced Way":

Like a bird in flight borne by its two wings, the practice of Dhamma is sustained by two contrasting qualities whose balanced development is essential to straight and steady progress. These two qualities are renunciation and compassion. As a doctrine of renunciation the Dhamma points out that the path to liberation is a personal course of training that centers on the gradual control and mastery of desire, the root cause of suffering. As a teaching of compassion the Dhamma bids us to avoid harming others, to act for their welfare, and to help realize the Buddha's own great resolve to offer the world the way to the Deathless.

Considered in isolation, renunciation and compassion have inverse logics that at times seem to point us in opposite directions. The one steers us to greater solitude aimed at personal purification, the other to increased involvement with others issuing in beneficent action. Yet, despite their differences, renunciation and compassion nurture each other in dynamic interplay throughout the practice of the path, from its elementary steps of moral discipline to its culmination in liberating wisdom. The synthesis of the two, their balanced fusion, is expressed most perfectly in the figure of the Fully Enlightened One, who is at once the embodiment of complete renunciation and of all-embracing compassion.

Both renunciation and compassion share a common root in the encounter with suffering. The one represents our response to suffering confronted in our own individual experience, the other our response to suffering witnessed in the lives of others. Our spontaneous reactions, however, are only the seeds of these higher qualities, not their substance. To acquire the capacity to sustain our practice of Dhamma, renunciation and compassion must be methodically cultivated, and this requires an ongoing process of reflection which transmutes our initial stirrings into full-fledged spiritual virtues.

Nirvana is the state of enlightenment in which one frees oneself from desire (and thus suffering). One who has achieved nirvana no longer suffers birth, aging, or death. When one who has achieved parinirvana, said individual is said to neither exist, neither not exist, neither both, nor neither.

Nirvana is not permanent, it is not impermanent, it is not both, nor neither. It is the ceasing of mental objectification, through the realization that all objectified things are impermanent, and not permanently satisfactory.

Only a person who sees Form or Essence sees Nirvana as a nihilism. But the Buddha never taught the annihilation of an existing being. He taught that existence and non-existence led to a thicket of views and no certain, permanent, arbiter. As such, concentrate on impermanence.

The main problem with the critique is that he doesn't distinguish tanha (i.e. craving or thirst) from chanda (i.e. desire, possibly wholesome desire). He therefore assumes that Buddhism is nihilist.

He also didn't mention "clinging", and so on.

In summary I think the critique is based on a false premise, i.e. it's a critique of his own (strawman) rendition of the four noble truths. You'd do better to study translations and commentary of the original version.

Another problem with it may be the statement, "However, there are two ways to deal with desire–one way is, as Buddhism suggests, to eliminate it. The other is to actually achieve what you desire." -- I'm not sure (but I doubt) whether that's acknowledging that sankharas are impermanent and unsatisfatory.

Another problem is, "How else can we be benevolent toward others other than by helping them to get the things they want or ought to want?" -- I think that's extremist, implying we might either try to satisfy everyone's every wildest dream, or care nothing for them ... instead there's a "middle way" (helping people with what they need, causing no harm, interacting harmoniously, and so on).

In the end it equates Buddhism with nihilism -- but Buddhism would describe nihilism as one of the types of Wrong View.

Avijjā does not know the ariya-sacca, such as:

Not knowing what desire is.

Not knowing what suffering is.

Not knowing what happiness is.

Not knowing what existence is.

Not knowing what non-existence is.

Not knowing what death is.

Not knowing what life is.

Not knowing all this, beings formulate views about all this.

They define what desire is, what suffering is, what happiness is, existence is, non-existence is, death is, life is, etc.

They say "This is X" not knowing that X is really not X. Not knowing the cause of why "that which is not X", becomes X.

Not knowing, they either fall to one of the two extremes:

"Something exists" is one extreme.

"Something does not exist" is the other extreme.

The article falls into the first, that of existence.

Since the author of the article likes existence very much, it is not surprising that when he/she studies the middle (neither existence nor non-existence), he interprets it as non-existence (nihilism), which neither Buddhists nor the Buddha would proclaim is the case.

Yes, for the one who is blind Buddhism is Nihilistic.

Imagine someone who has only a sense of touch, and you, having a faculty of sight, try to explain to him what the world of sight is, how would you explain it to him?

If he asks "is the color blue is rough or smooth or is it in between?" how would you answer? Would you not answer it’s neither rough or smooth, neither both, nor neither.

What would your friend think of your response? Would he not think you are completely talking nonsense? Why? Because for him the only world is the world sensed by touch.

And again if you told your blind friend that the surface he is been touching all his life is just a small turd and that if he doesn’t recover his sense of sight he will remain juggling the small turd all his life and will go nowhere.

What do you think your friend will say when you equate his world with a small turd? Would he not say you are a Nihilist? I think he will.

In the same way for Mr. Benjamin, Saṃsāra is the only world and when Buddhism describe Saṃsāra as perpetual suffering an endless cycle of birth, suffering, and death he would say Buddhism is Nihilistic.

Until Mr. Benjamin reflects deeply our existence in Saṃsāra and starts to see it as unsatisfactory any idea which negates his attachment (his attachment could be a desire for pleasure or fake sense of purpose or a hope from God) will be seen as Nihilistic.

I think only the Buddhist view can survive the deepest self-reflection that Nietzsche, the greatest proponent of nihilism, prophecies humanity will face soon.

Nietzsche said

I praise, I do not reproach, [nihilism's] arrival. I believe it is one of the greatest crises, a moment of the deepest self-reflection of humanity. Whether man recovers from it, whether he becomes master of this crisis, is a question of his strength!

Very standard critique, and very confused about Buddhism. Probably too much to unload in single post but here we go.

First, he does not understand what Buddhism means by "suffering". By suffering Buddhism means the painful state of discontent and frustration when things don't go the way we want and can't be easily fixed. Obviously, when you want something and it can be easily obtained, that's not suffering. When you're in an objectively difficult situation but you are at peace with it, that's not suffering either. That's just difficulty or pain. When you exercise and feel pain in the muscles, that's not suffering - because you wanted that. It's only suffering when your "is" conflicts with your "should" and you are helpless to fix it.

Second, "desire" is not as much sober aspiration/determination as it is the fruitless kind of obsession. When we obsess over a wish (positive), or over something we would like to stop (negative), we feel bad or we do some crazy stuff or both. No doubt about that.

Generally speaking, there are two approaches to discomfort: extensive and intensive.In one approach we turn on the heat - in the other we put on more clothes. In one we exterminate c**kroaches - in the other we keep the kitchen clean. In one we pave the wilderness with asphalt and build hotels - in the other we put on hiking boots and carry all food. In one we take medicine and do surgery - in the other we fix diet and lifestyle. In the same vein, when it comes to satisfaction with life, Buddhism says we must make our own mood. It is as simple as that. Instead of depending on external circumstances for happiness, we take charge of our own mood.

Nirvana as final death is a big misunderstanding. Nirvana is obtaining deathless. The deathless is obtained when we stop identifying with that which is subject to death. This is an act of making our own mood, an act of freedom. We choose to think that we are not this organism, nor are we the information that reincarnates from one organism to another. We don't identify with anything. Because we don't identify, we are not subject to death. Not subject to birth either. Hence "no more rebirth" and "final Nirvana". That's a simplification for kids. The real Nirvana is when we took charge of our mood, tamed our mind, and made it free from everything including death.

Now, on top of all that, some bright ancient people noticed that when people obsess with Buddhism, they tend to get antisocial, whether before they attain their peace or after. So they added this notion of compassion which was mentioned in the original teaching but not emphasized. They said, as you work on taking control of your mind and mood, why shouldn't you be nice to other people. And once you obtained your peace, why don't you help others. This fit surprisingly well with the teaching, and this is how Mahayana was born. Indeed, taking care of others is the best way to eliminate our mental fixations that cause our suffering in the first place, plus it helps reduce identification with "I" on the way to achieving the deathless.

All in all Buddhism is a very cohesive teaching where all elements fit together and help each other. The only thing to understand is that it is all about psychology of life, not life in this world but sentient life in general at any time any place in the universe.

That is not to say that this world is all we have. As we learn to see beyond preconceptions and become masters of mind, we start seeing things we could not see before. Training to be a master of mind, able to navigate layers of information, emotions, and energy without getting lost or confused is a way to that bigger world.