Givant and Halmos state p. 379 of their Introduction to Boolean Algebra:
The class of Baire sets of a $\sigma$-space is a $\sigma$-algebra, by definition. The subclass of meager Baire sets is naturally a $\sigma$-ideal in that algebra. It turns out that Baire sets are almost clopen sets in the sense that each Baire set differs symmetrically from a uniquely determined clopen set by a meager Baire set.
Since the meagre set in question is the boundary of some Baire set (which is even nowhere dense), why do we consider equivalence classes of Baire sets modulo the $\sigma$-ideal of meagre sets instead of equivalence classes of Baire sets modulo the ideal of nowhere dense sets?
Is it because in order that $\textrm{Ba}(X)/M$ be a $\sigma$-complete Boolean algebra (where $\textrm{Ba}(X)$ is the $\sigma$-field of Baire subsets of $X$), $M$ must necessarily be a $\sigma$-ideal?