One supposes that a big part of Ms Fallaci's dispair is driven by the steady increase in Moslem communities throughout Europe but especially in her native land. Islam is well on its way to a new wave of conquest, this time largely bloodless, of western countries through immigration and demographics. Moslems do not pay attention to the Club of Rome and Planned Parenthood about the need to not reproduce and they definately are not into zero population growth. In the sense that the west is up against a cultural entity that may be backward and incompetent but has boundless confidence in its dictums while Europeans have confidence in nothing and only want to be left alone to enjoy a life of materialist ease.
No, it has nothing to do with demographics. Her despair has a simple ideological root, not a pseudo-scientific one. She sees the west intellectually disarmed, refusing to defend the value of its own civilization and its achievements. She would not despair over anything so irrelevant as demographics, if people reacted naturally to direct attack by defense and counter-attack, to assaults on freedom by unapologetic defense of freedom as superior, etc.
She points out that in the days of facist Italy when blackshirts were roaming the streets, ready to beat anyone who dared to raise a voice against them, there was still backbiting and ridicule hurled at them. People were brave enough to stand up to them, when they had the whole government and ruthless force to face down. But now, when "the poor little dears" (Muslims) challenge anyone or anything, everyone gets out of their way, some scared of them directly, some even more scared of being called a racist for standing up to them.
To her that is an incomprehensible intellectual and civilizational suicide, a fundamental breakdown of elementary courage. That and that alone drives her to despair - of Europe and of Italy in particular, that is, not of the US. She does not despair for the US, although she does think even our reaction is far weaker than it ought to be. She is right about that. Everything is half-assed because of the level of unthinking opposition put up by the self-hating morons of the left.