Existentialism, Postmodernism and the Rabbi

Have a good week!
If I understand correctly, the reason the rabbi doesn’t like existentialism is because – although philosophy is not based on empirical observation, it can still be viewed with the ‘eyes of reason’ as the rabbi puts it (the truth is that this is the language of the ancients), and therefore it is not just a psychological experience, since existentialism is based only on experience, and therefore is a matter for psychologists and not philosophers.
But I think this is a mistake: 1- It is true that they describe a mental feeling, but it is based on a fundamental observation of the experience itself, i.e. it is not just a sensory description, but a fundamental characterization of the ‘subject’, thereby turning it into an ‘object’. And so, just as the Rabbi believes that it is possible to observe ideal axioms and from there analyze them conceptually and logically, so too is the experience.
I think what bothers the rabbi is not their philosophical description of man, but the solution they offer, which is that man can create his own meaning within himself. And in this the rabbi rightly argues, that this is a radical postmodern text that believes that truth and meaning are derived from man himself, and not outside of him. And this must be criticized just as all of radical postmodernism must be criticized (which not only claims that it is impossible to reach meta-truth, but that there is no truth, according to ethics and so on), that meaning and truth derived from man himself are not truth and meaning, but only experiences and narratives (although Schopenhauer already claimed that man has no meaning, unlike thinkers up until then who claimed that even if the meaning is not religious, it is still either moral or rational, and moreover, only through them is man realized, but he presented this in an analysis of the phenomenon and the noumena, and therefore he believed in a dual model, while existentialists speak in a material world, and as such they simply contradict themselves and so on).
2- I think that existentialist philosophy, as a matter of fact, has an important meaning, because it indicates (in analytical analysis) that there is a fundamental existential contradiction in man (and apparently this itself shows that man is different from animals and even perhaps proves that he is dual, since there is a fundamental contradiction in him between existence and meaning and existence).
Thank you very much.