SSA, SIA, and PBR
They are many ways to state SSA and SIA with equivalent effects on calculation. The following is just one version of it.
SSA: Treat yourself as a random sample of all actually existing (past, present, and future) observers in the reference class. It does not update on your own existence but favors situations where the fraction of observers with your epistemic situation is higher. E.g. "doom soon" in the doomsday argument.
SIA: Treat yourself as a random sample of all observers that could potentially exist. It considers your own existence more likely if there are more observers with your epistemic situation. So it updates on one's own existence and favors "big worlds" with more observers like you. E.g. presumptuous philosophers.
PBR: Do not start by thinking about "observers in my reference class" or "people in my epistemic situations". Instead directly start by recognizing "I am this person, living in this time". It is a datum that needs/has no logical explanation. PBR does not update on one's own existence, does not favor worlds with a higher fraction or higher number of observers in my epistemic situations.
There is no reason to "Who I am"
From each of us's natural first-person perspective, is there a logical explanation as to why I am this particular person instead of say, Bill Gates, a cow, a virus, or a neutron star? There is none. Yet that is the most fundamental fact I know of. I am this person because the only subjectivity available is due to it. I experience the world from its perspective.
From someone's perspective, the first-person "I" is inherently special. A twin does not need any information to differentiate himself from the other twin. Physical/epistemic similarities do not play any part in it. There is no "reference class" to the self at all.
Why do SSA and SIA feel so natural?
Because we are used to thinking from a god's-eye view. We like to conduct our reasoning "objectively": treating similar people with indifference. In most cases, this won't cause any problem. However, anthropic questions are formulated by using specific perspectives. The questions cannot be stated from the god's-eye view. So they have to be answered from those specific perspectives.
Take the doomsday argument for example. For the human species, "what kind of future shall we predict?" is a question dependent on who we are and when we live. Maybe Aristotle tried thinking about that during his time, but it would be a different problem from what we are trying to answer now. It should simply be answered with "I am this person, living during this time" as given. The prediction shall be solely based on the evidence I have.
However, if we take the "objective" god's-eye view and start by considering all human beings as logical equals (or potentially existing observers as equals), then there is the additional question of "why pay attention to me in the first place?". This is where the S*As kicks in: just treat me as a random sample. They provide the solution to a problem that doesn't exist.