I have the following definition, that is two vector fields $X$ and $Y$ commute if $[X,Y]=0$. There is result that states that two vector fields commute iff their flows do. This proposition is proved by using the following fact: given $F$ and $G$ the flows of $X$ and $Y$ respectively, we have that:
$$F_t \circ G_s (p)- G_s \circ F_t(p)=st[X,Y](p) + o (s^2 + t^2)$$
where $F_t$ and $G_s$ obviously mean the flow at times $t$ and $s$. This tells us that the bracket tells us "how much the two vector fields don't commute".
The question is: if the flows commute, it is obvious that $[X,Y]=0$. But for the other implication, why can I ignore the terms in $o(s^2 + t^2)$?