On the other hand, steelmaking also uses limestone as flux, to remove impurities from molten steel. When heated on the steel this drives off CO2. Calcium oxide could be used instead, but then that has to be sourced without CO2 emission, just as in cement manufacture.
I think there are at least two ways to make lime without CO2 emission. The first is normal limestone calcination, but with CO2 capture. The other is to use calcium silicate. This means dissolution of the silicate with hydrochloric acid, separation of silica, then high temperature reaction of calcium chloride with steam to produce lime and hydrogen chloride. I understand there's a company trying to commercialize this latter process.
And also, that carbon is not going into the atmosphere as carbon dioxide — it's going into the steel (as iron carbine and graphite IIIRC).