What will be the situation of the world when every beings will attain Nirvana? The ultimate goal of a Buddhist is to attain Nirvana, i.e., to stop the cycle of rebirth. Since a Buddhist is compassionate, she/he not only wants to stop her/his own rebirth but also wants that all beings will stop their rebirth. Now suppose this has happened: all beings have been able to stop the cycle of rebirth. Then what will be the picture of the world? There will be no life anywhere, let alone human civilization. The entire world will be like a land of the dead. Is that a desirable goal? If not, where is the fallacy in the above argument?
The Buddha explicitly declined to answer:


Whether or not the cosmos is eternal
Whether or not the cosmos is infinite
Whether or not the Tathagata exists after death


Cula-Malunkyovada Sutta


  And why are they undeclared by me? Because they are not connected with the goal, are not fundamental to the holy life. They do not lead to disenchantment, dispassion, cessation, calming, direct knowledge, self-awakening, Unbinding. That's why they are undeclared by me.


He seems to imply that both views are wrong view (or at least, not "right" view):


  It's not the case that when there is the view, 'The cosmos is finite,' there is the living of the holy life. And it's not the case that when there is the view, 'The cosmos is infinite,' there is the living of the holy life. When there is the view, 'The cosmos is finite,' and when there is the view, 'The cosmos is infinite,' there is still the birth, there is the aging, there is the death, there is the sorrow, lamentation, pain, despair, &amp; distress whose destruction I make known right in the here &amp; now.




If not, where is the fallacy in the above argument?

If you don't mind me saying so, a fallacy seems to be to be that you're postulating something good (i.e. "cessation of suffering"); and then proposing your attachment to and your imagination of something (i.e. "the picture of the world" and "the entire world" and "a land of the dead" and "a desirable goal") as a counter-argument; for example the following are meant as some absurd examples:


Suppose nobody needed to die anymore: how could grave-diggers then earn their living?
Suppose everyone's basic needs were magically taken care of, with enough food and shelter and protection from violence for everyone: society would collapse! Who would go to their jobs anymore? We'd be living in a world without slaves and without armies.