Hmm, I'm not sure there is an answer. If there is I have never heard it used.
The closest I can think if is indepdenent vs. dependent but that is more of a descripive distinction than a biological one.
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I considered altricial and precocial but it simply doens't answer the question.
Chickens and cows are the textbook precocial animals, the young are born well developed and can run and even feed themselves within minutes of being born. But chickens and cows certainly don't leave their mothers at birth. In fact both animals have come to symbolise motherhood and maternal care in western culture.
In contrast many fish are altricial and are born without functional mouths or any ability to feed themselves. Yet these species almost all leave the parent at birth, or simply hatch weeks after the parent has abandonded the eggs. They rely entirely on internal food reserves to survive until they are capable of feeding.
Any suggestion that all or even most precocial animals leave their nothers at birth is just plain wrong. And any suggestion that all altricial animals stay with the mother following birth is equally wrong.
It wouldn't surprise me if altricial and precocial are the answers the teacher is looking for, but they are in no way the correct answers to the question asked.