I guess most of us, in moments of existential crisis, have asked the question of "Why am I me?". It is not about grammar: "because 'I' and 'me' are both first-person singular pronouns." Nor is it a matter of tautology: "of course Bill Gates is Bill Gates. duh" It's the urge to question why among all things exist, I am experiencing the world from this particular being's perspective. How come I am not a different person, or animal, or some other physical entity.
Such a question does not have any logical explanation. Because it is entirely due to subjectivity. I inherently know this human is me because I know the subjective feeling of that person. Pain can be logically reduced to nerve signals, colors by wavelength. Yet only when this human is experiencing them will I have the subjective feeling. Explaining "Who I am" is beyond the realm of logic. It is something intuitively known. An axiom.
So rational thinking should have no answers to questions such as "the chances of me being born as a human". I'm a human is a fact that can only be accepted, not explained. However, when framed in certain ways, similar questions do seem to have obvious answers. For example, "There are 7.7 billion people in the world, about 60% Asian. What's the probability of me being an Asian ?" Many would say 60%.
That's because it is uneasy to have no answer. So we often subconsciously change the question. Here "I/me" is no longer taken as the axiomatic, subjectively defined perspective center. Instead used as a shorthand for some objectively defined entity, e.g. a random human. By using an objective reinterpretation, the question falls back into the scope of logical thinking. So it can be easily answered: since 60% of all people are Asian, then a randomly selected person should have a 60% chance of being one.
Mixing the subjectively defined "I" to objectively defined entity seldomly causes any problem. Anthropic reasoning is an exception. Take the Doomsday Argument for example. It is true a randomly chosen human would be unlikely to be the very early ones. If it turns out so, the Bayesian update to doom-soon would be valid too. However, the argument uses words such as "I" or "we" as something primitively understood: the intuitive perspective center. In this case, probabilities such as "me being born as the first 5% of all human" have no answer at all. Because "who I am" is something that can only be accepted not explained, an axiom.