In goes iron ore, a mix of iron oxides and carbon, out comes iron and carbon oxides. The carbon moved from the ore to the atmosphere.
So if I recall correctly from HS chem, iron is being reduced in this case by the carbon in the coke. From a cursory glance at the electronegativity table, iron is at 1.83, carbon's at 2.5 and hydrogen is 2.1. Higher electronegativity = more attractive to electrons = better reducing agent so hydrogen will reduce iron but less efficiently? than carbon. I don't know if this means that more energy is required to get the hydrogen to reduce carbon, or if the reaction will just be slower, but the upside is that the only byproduct of this process is pure H2O.
You push a lot of carbon into the iron, most react with oxygen and go away as CO2. So the entire process emits CO2, and absorb pure carbon (usually from oil).