[pbsd]

Collision resistance implies 2nd-preimage resistance, and is therefore the stronger notion.

Suppose your function is collision resistant, but not 2nd-preimage resistant. Then this means we cannot find an arbitrary pair (x, y) such that H(x) = H(y). But given a fixed x, H(x) we can find y such that H(y) = H(x). This is of course absurd, since we can easily turn the latter 2nd-preimage attack into a collision attack by fixing some arbitrary x ahead of time.

It is also the case in practice that collisions are easier to find. This is owed to the fact that a collision attack has much more degrees of freedom given to the attacker than a (second) preimage attack.