Menger's theorem is stated as:
Let $G$ be a connected graph, and $a,b$ distinct non-adjacent vertices of $G$. If all $a$-$b$ separators have size $\geq k $, then there exists a family of $k$ independent $a$-$b$ paths.
A remark then says that "note that you cannot prove Menger by choosing one point on each path in a maximimum-sized "family of independent $a$-$b$ paths"." I don't understand what this statement is saying, at all. Any explanation would be appreciated. Thanks
EDIT: I think I've answered my original question in the comment below, but I have another related question. My notes state that an equivalent form is "minimum size of an $a$-$b$ separator = maximum number of independent $a$-$b$ paths". I don't see how this is equivalent; if the minimum size of an $a$-$b$ separator is $k$, why can't there be $k+1$ independent paths?