I'm following a course on differential geometry and from some background I've gotten used to the fact that a topological manifold $M$ is called a smooth/differentiable manifold if we can equip $M$ with some smooth atlas $\mathcal{A}$, then the pair $(M, \mathcal{A})$ is called a differentiable manifold.
Now reading Lee's book I've found out that we actually require $\mathcal{A}$ to be something called maximal. He first states that
Our plan is to define a “smooth structure” on $M$ by giving a smooth atlas, and to define a function $f : M \to \Bbb R$ to be smooth if and only if $f \circ \varphi^{-1}$ is smooth in the sense of ordinary calculus for each coordinate chart $(U, \varphi)$ in the atlas. There is one minor technical problem with this approach: in general, there will be many possible atlases that give the “same” smooth structure, in that they all determine the same collection of smooth functions on $M$.
Then he goes on to state that
However, it is more straightforward to make the following definition: a smooth atlas $\mathcal{A}$ on $M$ is maximal if it is not properly contained in any larger smooth atlas. This just means that any chart that is smoothly compatible with every chart in $\mathcal{A}$ is already in $\mathcal{A}$.
The lecturer in the course I'm taking says that in practice we only need to consider some atlas $\mathcal{A}$ for $M$ instead of the maximal one which is causing my confusion. Why is this true?
Lee also gives the proposition $1.17$ which states that
Let $M$ be a topological manifold, then every smooth atlas $\mathcal{A}$ for $M$ is contained in a unique maximal smooth atlas, called the smooth structure determined by $\mathcal{A}.$
and presumably this is the reason why we can consider some arbitary atlas $\mathcal{A}$ instead of the maximal one?
Why does this imply that we don't need to consider the maximal one? I don't think it's obvious.