I'll phrase my confusion in the context of the Prisoner's Dilemma (although it is applicable to other situations).
There are two "rational" players $A$ and $B$, each faced with a decision between options $X$ and $Y$. The payoff matrix is,
$$ \begin{array}{|c|c|c|} \hline (A\text{ payoff},B\text{ payoff}) & A\text{ chooses }X & A\text{ chooses }Y\\ \hline B\text{ chooses }X & (a,a) & (b,c) \\ \hline B\text{ chooses }Y & (c,b) & (d,d) \\ \hline \end{array} $$
Where $b > a > d > c$. As the usual reasoning goes, if player $A$ chooses $X$, then player $B$ should choose $Y$ since $b > a$. If player $A$ chooses $Y$, then player $B$ should again choose $Y$, since $d > c$. Thus, player $B$ should always choose $Y$; by similar reasoning, player $A$ should always choose $Y$.
My confusion comes from the fact that the situation is symmetric. Since $A$ and $B$ are both rational players in a symmetric situation, if there exists a single best choice, that choice must be the best choice for both players. From what I understand, in game theory it is assumed that all players have shared information and all players know that the other players are rational. But this would imply that $A$ and $B$ have the information necessary to conclude that they will both make the same choice. Thus, they are now faced with two outcomes: choose $X$ and receive payoff $a$, or choose $Y$ and receive payoff $d$. Since $a > d$, they would both choose $X$.
What is wrong with this reasoning? Are they not given the knowledge that all other players are rational? Are they somehow forbidden from "meta" reasoning like this; and if so, what constitutes "meta"?
A rational player is seeking to maximize their own play, without concern for how it affects others. Indeed, rational play pushes the players toward $(d,d)$, because there's no reason not to -- whether I'm guessing what player A will do, or player A acts first and explicitly reveals their action, I'm better off choosing Y.
Rational players don't see a reason to cooperate unless the incentive to do so is greater (ie, if $a>c$ and $b>d$).
What you're thinking about, with this "meta reasoning" discussion, is what's known as a hyper-rational player. Hyper-rational players can look at outcomes based on how they affect everyone at the table, and can consider whether looking out for everyone is a better strategy. This act of "looking at everyone" is needed to escape the mutually assured destruction of $(d,d)$, and allows the hyper-rational player to consider that if everyone plays X, everyone is better off in the long run.
The reason that rational players won't do the same thing is because the hyper-rational move isn't a stable one. Once you know that everyone will agree to play X, the rational player realizes that if he's the only one that plays Y, he will cash in big... (and so on, and so on.)