The way your source puts it, is very misleading.
Logical empiricists had nothing against "metaphysical poetry". This seems to be a recurring misunderstanding. Indeed, according to logical empiricists, poetry is one of the best suited media to express "mystical longings".
Long explanation (by Carnap himself)
The whole point is clearly stated by Carnap in his paper on the "Elimination of metaphysics through logical analysis of language" (1932), esp. §7 "Metaphysics as expression of an attitude towards life":
[…] We find that metaphysics also arises from the need to give expression to a mans's attitude in life, his emotional and volitional reaction to the environment, to society, to the tasks to which he devotes himself, to the misfortunes that befall him. This attitude manifests itself, unconsciously as a rule, in everything a man does or says. It also impresses itself on his facial features, perhaps even on the character of his gait. Many people, now, feel a desire to create over and above these manifestations a special expression of their attitude, through which it might become visible in a more succinct and penetrating way. If they have artistic talent they are able to express themselves by producing a work of art. Many writers have already clarified the way in which the basic attitude is manifested through the style and manner of a work of art (e.g. Dilthey and his students).
[In this connection the term "world view" ("Weltanschauung") is often used; we p refer to avoid it because of its ambiguity, which blurs the difference between attitude and theory, a difference which is of decisive importance for our analysis.]
What is here essential for our considerations is only the fact that art is an adequate, metaphysics an inadequate means for the expression of the basic attitude. Of course, there need be no intrinsic objection to one's using any means of expression one likes. But in the case of metaphysics we find this situation: through the form of its works it pretends to be something that it is not. The form in question is that of a system of statements which are apparently related as premises and conclusions, that is, the form of a theory. In this way the fiction of theoretical content is generated, whereas, as we have seen, there is no such content. It is not only the reader, but the metaphysician himself who suffers from the illusion that the metaphysical statements say something, describe states of affairs. The metaphysician believes that he travels in territory in which truth and falsehood are at stake. In reality, however, he has not asserted anything, but only expressed something, like an artist. That the metaphysician is thus deluding himself cannot be inferred from the fact that he selects language as the medium of expression and declarative sentences as the form of expression; for lyrical poets do the same without succumbing to self-delusion. But the metaphysician supports his statements by arguments, he claims assent to their content, he polemicizes against metaphysicians of divergent persuasion by attempting to refute their assertions in his treatise. Lyrical poets, on the other hand, do not try to refute in their poem the statements in a poem by some other lyrical poet; for they know they are in the domain of art and not in the domain of theory.
Perhaps music is the purest means of expression of the basic attitude because it is entirely free from any reference to objects. The harmonious feeling or attitude, which the metaphysician tries to express in a monistic system, is more clearly expressed in the music of Mozart. And when a metaphysician gives verbal expression to his dualistic-heroic attitude towards life in a dualistic system, is it not perhaps because he lacks the ability of a Beethoven to express this attitude in an adequate medium? Metaphysicians are musicians without musical ability. Instead they have a strong inclination to work within the medium of the theoretical, to connect concepts and thoughts. Now, instead of activating, on the one hand, this inclination in the domain of science, and satisfying, on the other hand, the need for expression in art, the metaphysician confuses the two and produces a structure which achieves nothing for knowledge and something inadequate for the expression of attitude.
Our conjecture that metaphysics is a substitute, albeit an inadequate one, for art, seems to be further confirmed by the fact that the metaphysician who perhaps had artistic talent to the highest degree, viz. Nietzsche, almost entirely avoided the error of that confusion. A large part of his work has predominantly empirical content. We find there, for instance, historical analyses of specific artistic phenomena, or an historical-psychological analysis of morals. In the work, however, in which he expresses most strongly that which others express through metaphysics or ethics, in Thus Spake Zarathustra, he does not choose the misleading theoretical form, but openly the form of art, of poetry.
Or, as Gottfried Gabriel once put it:
With Carnap, so to speak, Frege's Begriffsschrift lies on the desk and Nietzsche's Zarathustra on the bedside table.