You can't have logic without axioms, a foundation that can't be proven, but is accepted. 'Reality is real' is an unspoken axiom/premise of almost every logical argument dealing with reality, for instance. It is not a fault of ethics that it can't prove its logical foundations, even physics can't do that (prove that reality is real). Harris didn't get from an 'is' to an 'ought', but 'what is best for human thriving' certainly isn't the worst or most difficult to accept axiom on which to base a moral system.
I'm not anti-Christian. I'm anti-stupid.