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Sorry accidentally hit thumbs down went i ment to hit thumbs up

Probably to make sure his dad and older brother don't get a chance to force him to leave behind the the cockatrices.

I think because he wanted to leave on his own terms. The parents were more than willing to make use of him (eggs, watching his siblings etc), but not ready to invest in him long-term. So there is no way that they would let him leave with the very useful resources such as friendly cockatrice. And if he had waited until he was longer, he might have been kept under stricter watch to make sure that he doesn't leave with more than they were willing to give him.