Obviously (2) does not follow from (1). As any human being learns early on, just because we want something, that does not mean that we can have it. Consider an analogous argument: (1) Human beings desire the power to predict the future. (2) Therefore, human beings can predict the future. Anyone can see that this is not a good argument.
Giving Buber the benefit of the doubt, we can probably conclude that he had no intention of putting forward such an obviously flawed piece of reasoning. Instead, he must have had something else in mind. But what could this have been? There are several possible alternatives. First, he might have wanted the wording of (1) to be much stronger; instead of "want", perhaps he would have substituted "need" so that the premise reads like this: (1') Human beings have a need for a spiritual relationship. Then, he might have added another premise: (2) The construction of the human psyche cannot be flawed. In other words, if we have a basic psychological need, then we must have the means to satisfy that need. Only then would he conclude, (3) Therefore, human beings can enter into such a relationship.
But why believe that the construction of the human psyche cannot be flawed? There are a few plausible reasons that Buber might have felt justified in believing this. It is likely that he based this belief on his belief in God: God would not have created us with a need that we could not satisfy. Of course, then Buber would need a proof for the existence and nature of God to back up his claim. However, this is not Buber's main object and as such he does not provide such a proof.
Perhaps, however, Buber was not trying to make a rigorous argument and his purpose in tracing the origin of our basic need for relation was not to prove that we have this mode available to us. Perhaps it was simply to trace the origin for the sake of tracing the origin. That would leave Buber without any proof for the claim that we actually do have this mode available to us, but that is not necessarily a problem for him: instead of providing us with an a analytic, philosophical proof, he might want us to engage in our own, introspective proof. To see that we have this mode available to us, he might say, we should just try to use it.
Turning now to the two arguments for the claim that relation is primary, a few more worries arise. Buber seems correct in his claim that both primitive languages and the language of early children seem to reveal a more heavily relational aspect. The separation between subject and object is not as clearly demarcated. The question is whether these aspects of language have the drastic implications that Buber believes they do. It seems plausible that the worldview behind these relation-heavy languages is more relational than the worldview behind our distinction-heavy language, but is it really as purely relational as Buber claims? This question cannot be answered by reasoning alone; it requires more observational evidence.
The same can be said for Buber's analysis of infant behavior. Perhaps he is right to claim that infants are yearning for relation when they reach out their hands, stare at walls, and gurgle to no one in particular, but he offers no truly compelling reasons to trust him on this. There are numerous alternative explanations available for these patterns of behavior, all of them equally or more plausible than Buber's explanation. For instance, the infants might simply be exercising their newly-forming faculties. Again, Buber never gives his claims the rigorous proof that is required to accept them without further experience.