Carbon or Hydrogen - How best to process Ilmenite?

>From my reading of the material that's often quoted about the best
way to process ilmenite, there is a lot of reference to hydrogen
being used, but I can't really see the benefits.

Carbon will reduce ilmenite and combine with 1.25 times its own mass
per heating cycle, thereby eliminating a need to use the furnace for
multiple heating cycles as would be required with hydrogen, because
hydrogen is limited to only .4-.9 times its own mass.

Further, carbon leakage can be made up for with materials shipped
from earth. Packing material can have high carbon content. Hydrogen
has to be cryogenic.

The technology for processing steel and lowering the carbon content
are well established. Nobody is processing steel with hydrogen
reduction. The residual hydrogen leaves the steel very brittle.

I would say that the primary use for hydrogen on the lunar surface
should be to produce water. Carbon should be used for the materials
processing and the resultant carbon monoxide and carbon dioxide can
be separated into their constituent elements for re-use.

I don't understand why hydrogen is touted so aggresively.