What is the logic behind "young are born alive"? Can it be born dead?

It means, as opposed to hatching from eggs as in the case of birds or reptiles.

By the way, mammalian offspring can be "born dead," it is called a stillbirth. Otherwise, see Gunga's response.

True that occur sadly in my family when my full term sister was stillborn due to her umbilical cord wrapping around her neck near the very end of her last term.

In this context 'born alive' means expelled at birth from the mother's body fully functioning and able to lead an autonomous existence, not in an egg. Monotremes are mammals that lay eggs instead of giving birth to live young.