Why would the loss of H₂ to space mean that the Earth's geochemistry would be based on acid/base reactions?

I am reading a paper[1] that contains the line:

Most of the $\ce{H2}$ in the Earth's mantle escaped to space early in the Earth's history; consequently, the overwhelming majority of the abiotic geochemical reactions are based on acid/base chemistry, i.e., transfers of protons without electrons.

The connection between the loss of $\ce{H2}$ and acid/base chemistry is not clear to me.

Why would the loss of $\ce{H2}$ to space make acid/base chemistry the default?

1. Falkowski, P. G., T. Fenchel, and E. F. Delong. (2008) The microbial engines that drive Earth's biogeochemical cycles. Science 320:1034-1038.
• I think what is happening here is this... we know we have abundant H2 gas today, so where did it come from if all the H2 gas disappeared in the early stages of the Earth? I'm going to over-simplify the answer to this question. The author is alluding to acid-base chemistry as the explanation for the existing H2 gas, so it seems. – LordStryker Aug 28 '12 at 14:46
• I edited the LaTeX out of the title for indexing purposes, as the markup would end up showing on search engines, etc., otherwise. – jonsca Aug 28 '12 at 22:51

before life existed the atmosphere contained mainly $\ce{N2}$, with negligible $\ce{O2}$, probably more $\ce{CO2}$ than today, and only minor levels of reducing gases such as $\ce{H2}$.
So, in the absence of widely available gases such as oxidative $\ce{O2}$ or reducing $\ce{H2}$, oxygen was mainly present as $\ce{H2O}$ and $\ce{CO2}$. This means redox reactions are not big players in the overall chemical scheme of the periodic atmosphere, and acide-base reactions dominate (by default).