Sacred Haven of Debauchery

I don't understand why griffins, having a "lion's rear," can't lay eggs.

Are you trolling or what? A lion is a mammal. A lioness has a uterus from which lion cubs are born. Then she feeds them with breast milk. The uterus is not in the head or in the front paws. The griffin has a lion's rear. This means it has a uterus and mammary glands. A griffin should give birth to half a dozen griffon chicks at once and then feed them in its rooster's nest with breast milk. The fact that its front part is from a bird only means that it has difficulty chewing food and that it is somewhat dull.
Why doesn't it lay eggs then? What the hell?
Although, I shouldn't even be talking about this with you.

Added 1 minute ago
One gene and self-suggestion won't achieve anatomical transformation of the organism.