In this cool video of a presentation about SpaceX's GPU-based computational fluid dynamics, there is a slide early on about making rocket fuel on Mars - specifically using water from the ground and carbon dioxide from the atmosphere to make oxygen and methane:
2H2O + CO2 -> CH4 + 2O2
Going in that direction requires energy, and I'm guessing solar power in some form or other would certainly be one way.
But why not keep it simple ("because it isn't" is a possible answer) and just use solar photovoltaics and electrolysis to make LOX and LH2 from the same water used above:
2H2O -> 2H2 + O2
What are the salient tradeoffs here? If the slide shows methane, and the acompanying discussion talks about the problems of trying to make a methane engine, why is LOX + LH2 not discussed?