A controlling factor is a factor that acts as a cause for others. A reactive factor is rather the consequence: that which reacts to the controlling factor.
For example, the Sun is certainly a controlling factor. Nothing we do influences what happens on the Sun, but what happens on the Sun certainly influences us very strongly. Fortunately, its total power output is quite stable so as far as climate is concerned, we don't need to worry about it too much as far as the next couple of million years are concerned (although eventually, in hundreds of millions to billions of years, increasing power from the Sun will render the Earth uninhabitable).
CO₂ is both a controlling and a reactive factor. We add CO₂ to the atmosphere, so the CO₂ concentration reacts to our emissions (reactive factor). But CO₂ levels are also a cause. If you were to make a simple climate model, you would put in the CO₂ concentration as a fixed value or perhaps an increasing value as a function of time: in such a model, it would be a boundary condition. If you instead made a model of a single factory or car and modelled how changes in the fuel cycle would affect CO₂ emissions, then those would instead be a reactive factor. It all depends on the context.
For H₂O, however, it makes no sense to put in a fixed version as a boundary condition. Its concentration varies rapidly on short timescales: today may be dry and tomorrow a wet airmass may get in. Of course, physically, H₂O causes even more of the greenhouse effect than CO₂, but the increase of H₂O is not what is causing anthropogenic climate change; if anything, an increase in H₂O is one of the effects.
So, think of it as a system: you add CO₂ (cause), many things happen, including an increase in H₂O in some places (effect). The cause is the controlling factor. The effect is the reactive factor, even though physically, both CO₂ and H₂O are strongly contributing greenhouse gases.