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"If life begats life, how does non-life begat life?"

It all depends on what you mean by "life." What most creationists think of when they say "life" is a mystical invention that we have no good reason to believe even exists.

But when scientists speak of "life," they generally do it with the fill understanding that the boundary between life and non-life is arbitrary. Our planet has on it things that are unambiguously living, things that are unambiguously non-living, and things that lie somewhere on a continuum in between.

For example... is a virus "living?" How about a bacterial spore? How about prions?

In short... there is no good reason to accept "life begats [sic] life" as an axiom. It is merely a general rule for which there are exceptions.