The point would be that what I call “me”, and what I know of “me”, is conditioned by the presence of various cravings, fears, delusions, and such – or, in Catholic terms, concupiscence. Such a “me” cannot in itself produce a “me” free of cravings, fears, delusions, and such. However, this “me” can “co-operate” with those other persons (called Buddhas, or Bodhisattvas, or Arhats, or what not) who are free of cravings, fears, delusions, and such – and this “co-operative engagement” can lead to the offering of this “me” into the fire of Nibbana.
But I can do none of this on my own. Thus, taking refuge is essential.