For physicists, the term "detailed balance" is used in one of the following contexts:

1. A closed system A is observed at a coarse-grained level (e.g. A is a vessel with a macroscopic amount of chemicals, yet one only tracks/observes the global concentrations of the chemicals).

An observable system A (e.g. a mixture of chemicals) is weakly in contact with an external "bath" B. The latter is in thermodynamic equilibrium.

Microscopically then, the contents of A resp. A+B must obey deterministic, time-reversible equations of motion. Careful: when we hit the rewind-button for the motion of a particle in time, its instantaneous position $x$ is not changed, but its velocity $v$ of course flips to $-v$. The former variables are called "odd" and the latter are "even" under time-exchange. Now, when the global system ($A$ resp. $A+B$) is in thermal equilibrium, every microscopic trajectory has the same likelihood as the time-reversed trajectory. So microscopically the probability to see a certain transition-event from a micro-state $\alpha$ to $\beta$ is equal to the probability to see a transition from $\beta$ to $\alpha$. For our macroscopic observations (concerning $P_{i \to j}$, it remains simply to count the number $W(i)$ micro-states $\alpha$ that correspond to a certain macrostate $i$. The $\log$ of this microstate-multiplicity of the macrostate $i$ is precisely the entropy/ free energy (depending on the context) $G(i)$. Also there's the multiplication of the log by $k_B T$. We then obtain $$1=\frac{W(i)P_{i \to j}}{W(j')P_{j' \to i'}}=\frac{W(i)P_{i \to j}}{W(j)P_{j' \to i'}}.$$ So $$\frac{P_{i \to j}}{P_{j' \to i'}}=\frac{W(j)}{W(i)}=e^{\frac{G(j)-G(i)}{k_BT}}.$$ To proceed finally to your question why in the context of chemical kinetics, the time-reversed state $i'$ of $i$ is simply $i$: You presumably keep track of the macroscopic concentrations of your chemicals and those data are the content of your states {i}. Now, since the microscopic positions of particles are even under time-exchange, also concentrations of those particles in a fixed region of space are even variables. So indeed, upon applying time-reversal, an array of concentrations $i$ remains the same array of concentrations $i$.

For physicists, the term "detailed balance" is used in one of the following contexts:

1. A closed system A is observed at a coarse-grained level (e.g. A is a vessel with a macroscopic amount of chemicals and one only tracks/observes the global concentrations of the chemicals).

An observable system A (e.g. a mixture of chemicals) is weakly in contact with an external "bath" B. The latter is in thermodynamic equilibrium.

Microscopically then, the contents of A resp. A+B must obey deterministic, time-reversible equations of motion. Careful: when we hit the rewind-button for the motion of a particle in time, its instantaneous position $x$ is not changed, but its velocity $v$ of course flips to $-v$. The former variables are called "odd" and the latter are "even" under time-exchange. Now, when the global system ($A$ resp. $A+B$) is in thermal equilibrium, every microscopic trajectory has the same likelihood as the time-reversed trajectory. So microscopically the probability to see a certain transition-event from a micro-state $\alpha$ to $\beta$ is equal to the probability to see a transition from $\beta$ to $\alpha$. For our macroscopic observations (concerning $P_{i \to j}$, it remains simply to count the number $W(i)$ of micro-states $\alpha$ that correspond to a certain macrostate $i$. The $\log$ of this microstate-multiplicity of the macrostate $i$ is precisely the entropy/ free energy (depending on the context) $G(i)$. Also there's the multiplication of the log by $k_B T$. We then obtain $$1=\frac{W(i)P_{i \to j}}{W(j')P_{j' \to i'}}=\frac{W(i)P_{i \to j}}{W(j)P_{j' \to i'}}.$$ So $$\frac{P_{i \to j}}{P_{j' \to i'}}=\frac{W(j)}{W(i)}=e^{\frac{G(j)-G(i)}{k_BT}}.$$ To proceed finally to your question why in the context of chemical kinetics, the time-reversed state $i'$ of $i$ is simply $i$: You presumably keep track of the macroscopic concentrations of your chemicals and those data are the content of your states {i}. Now, since the microscopic positions of particles are even under time-exchange, also concentrations of those particles in a fixed region of space are even variables. So indeed, upon applying time-reversal, an array of concentrations $i$ remains the same array of concentrations $i$.