Vocal production learning and beat perception and synchronization (BPS) share some common characteristics, which makes the vocal learning and rhythmic synchronization hypothesis (VLH) a reasonable explanation for the evolution of the capability for rhythmic synchronization. However, even in vocal learners, it is rare to see non-human animals demonstrate BPS to human music. Therefore, the first objective of this article is to propose some possible reasons why we do not see BPS in budgerigars, an excellent vocal learning species, while presenting some of my own findings. The second objective of this article is to propose a seamless bridge to connect the capability for vocal learning and BPS in locomotion. For this purpose, I present my own findings, wherein cockatiels spontaneously sang in synchrony with a melody of human music. This behavior can be considered a vocal version of BPS. Therefore, it can establish a connection between these two capabilities. This article agrees with the possibility that some mechanisms other than the vocal learning system may enable BPS, contrary to the original idea of VLH. Nevertheless, it is still reasonable to connect the capability for vocal learning and that for BPS. At the very least, the capability for vocal learning may contribute to the evolution of BPS. From these arguments, this article also proposes a scenario which includes vocalizing in synchrony as a driving force for the evolution of BPS and the capability for music production.