Does cryptographically-secure pseudo random generators require a secure seed?
Actually, your second sentence itself is the answer. A pseudo random number generator(cryptographically secure or not) is a deterministic algorithm which produce random looking numbers. Every time you provide the same seed it produces the same random looking numbers. Now, if your seed value is predictable and algorithm is public then the output of the deterministic algorithm is also predictable. So, the seed of a cryptographically secure pseudo random number generator must be secret, so that the output you get is unpredictable.