I assume "any parent" means the mother. If the father deposits the baby without the mother's knowledge, that would be illegal. If the mother deposits the baby without the father's knowledge, that's okay.
Why would you assume that?! The law could have simply stated "the mother can leave..." and thus removed all doubt. What in the wording here led you to infer that "fathers" were excluded? Where is there any mention of the parent's sex?
Regards,
For the same reason that a woman can abort a child without the father's consent.
So yes, I assume that a mother can deposit a baby without the father's consent, whereas the reverse is not true.
"Any parent" means the baby can be left by any parent, but only subject to the mother's choice.