The chemical formula for ilmenite is FeTiO3 (Fe is iron, Ti is titanium an O is oxygen).
This means that the amount of iron = the amount of titanium in ilmenite, so logically any reaction that refines ilmenite should produce equal amounts of both metals (and 3 times as much oxygen).
The problem is that you can easily strip the iron from ilmenite in a blast furnace, but you can not strip the titanium (or the oxygen) from the ilmenite through the same reaction. It goes something like ilmenite + coke + flux > pig iron* + slag (rich in Ti, basically it is everything in the ilmenite that was not iron + everything in the flux + residue of the coke). You can then chemically treat the slag with acids, bases and other fun stuff to get TiO, TiO2 (rutile), TiO3 (and a different kind of slag) which you can then feed into the rutile > titanium process.
The big problem is that titanium is very reactive with oxygen (just like aluminum), more so than iron or carbon (you can strip the oxygen from iron ore, all iron ores are Fe#O#, because the oxygen would rather hang out with the carbon than the iron, oxygen would rather hang out with titanium and aluminum than carbon, which is why pre-industrial tech can't smelt those ores and why you need the acids, bases and catalysts to refine them).
You can however reduce (strip the oxygen from it) ilmenite with coke to FeCTi (very hard, very brittle ceramic substance) which can be used to make Ti rich Alloy Steels (relatively rare, search ferrotitanium) or cutting tools.
You can also reduce rutile with copper or manganese (copper makes cuprotitanium, rather like a bronze made with aluminum; manganese makes manganotitanium which can be used to make Alloy Steels or further refined to the pure metals).
This is one of those situations where you have to get it stupidly hot to reduce it (like bauxite) or you have to perform some chemical tricks to get what you want out of it.
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* just the way blast furnaces work they make pig iron which is then converted into iron and steel
