Yet again, Craig does a fine job of illustrating what the basic fallacy is, which makes it all the more baffling that he commits them so frequently and so flagrantly.
He acknowledges that the argument as I laid it out above would be "manifestly fallacious". He then claims that the real reasons he thinks "everything that begins to exist has a cause" is for the following reasons:
1. Something cannot come from nothing
2. If something can come into being from nothing, then it becomes inexplicable why just anything or everything doesn't come into being from nothing.
3. Common experience and scientific evidence confirms the truth of (1)
Where Craig goes wrong with regard to (1) is when he says the following:
If you deny premise one, you've got to think that the whole universe just appeared at some point in in the past for no reason whatsoever.In his examples justifying (2), Craig falters by conflating "without a cause" with "coming from nothing". They're not the same thing. I'll have more to say on that later in the series.
Being someone who studies cosmology and often makes a show of citing physicists, Craig ought to know better. No non-believer claims that the universe came from nothing – at least not in the sense of "absolute nothing" Craig uses. Further, it's nonsensical to say that the universe would have "appeared at some point in the past" because, if the universe did not exist, then there was no time in which it could begin to exist*.
But the bigger obstacle for Craig is that modern physicists believe the universe could exist uncaused. These include Alexander Vilenkin's quantum-tunneling model, the Hawking-Hartle No Boundary Proposal, as well as a litany of possibilities from String Theory and Loop Quantum Gravity. Even if the observable universe has a beginning at the Big Bang, a theory of quantum gravity may show that the universe evolved from a prior state that was timeless and causeless. The fact that we do not yet know demonstrates two things: that we must remain agnostic regarding the origin of the universe, and that there is insufficient evidence to claim the universe requires an external cause.
So, does Craig commit a fallacy of composition? Yes. That's because even if we're so kind as to grant him the straw-man arguments he laid out above (1-3), those principles are still inferred purely on the basis of observation of physical reality. Craig's own third proposal – that scientific evidence confirms the truth – backfires, because science is rooted in epistemic naturalism. Craig still has not given us any reason to believe that anything inferred by observation within the universe must also apply to the universe.
*Notably, Craig gets around this much in the same we he tries to dodge the causality dilemma: by proposing the existence of a speculative non-physical time 
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