Why does knowing the number of points on a curve help solve ECCDLP?
Actually, we don't count points to attempt to break Elliptic Curves, a major reason we count points is to ensure that we can't.

If the number of points on the curve is $n$, then we know how to solve the ECCDLP problem in $\sqrt{n}$ time.  However, if we know a factorization $n = pq$, then we can use that factorization to solve the ECCDLP problem in $\sqrt{p} + \sqrt{q}$ time.  Note that this is distinctly smaller; if $n$ is 256 bits, then $\sqrt{n}$ is 128 bits; we believe that no one has the computational resources to do $2^{128}$ work.  On the other hand, if $p$ and $q$ is 128 bits, then $\sqrt{p} + \sqrt{q}$ is about 65 bits; we know that performing $2^{65}$ work is achievable in practice.

To avoid this potential problem, we generate curves until we find one with a prime number of points on it (or, a prime times a small cofactor); once we have that, the above observation is of no use to an attacker.

Now, that's not the only reason knowing the number of points on a curve is useful, however it is a major one.