Is water vapour a product of fossil fuel oxidation?
Althugh water vapor contributes to greenhouse warming of the atmosphere, changes in atmospheric water vapor tend to follow rather than drive changes in temperature. Also, in the form of clouds, atmospheric water can have a cooling effect on earth temperature.

Clouds illustrate why water vapor, unlike carbon dioxide and methane, is not thought of as a driver of recent changes in earth temperature but rather is more of a follower. Unlike those other two gases, if you keep trying to put water vapor gas into the atmosphere it will convert to liquid water at some point, leaving only a constant level of water in the form of gas. That's what happens when a cloud forms; what you see and what can shield you from the sun is a collection of water droplets or ice crystals. Large amounts of water vapor are also regularly put into the atmosphere by evaporation of water from the earth's surface, dwarfing the contribution from human respiration. Eventually the atmosphere gets locally saturated with water vapor and it falls back to earth as rain or snow in the hydrologic cycle.

In principle methane and carbon dioxide could similarly condense out of the gas phase, but not at temperatures that occur in our atmosphere. You need to go far out into cold reaches of the Solar System to find naturally occurring methane lakes or solid carbon dioxide. There is no equivalent of rain to remove excess of those gases from our atmosphere. Carbon dioxide can dissolve in water to leave the atmosphere, but at the cost of acidifying the water. Ocean acidification is another serious result of adding carbon dioxide to the atmosphere.

The amount of vapor you can add before conversion to liquid water increases with the temperature. So as land temperature increases the rate of evaporation of water into the atmosphere can increase, and as atmospheric temperatures increases the amount of water vapor that the atmosphere can hold also increases. So in principle water vapor might thus serve to amplify the greenhouse warming from other gases, although its transition to liquid or ice in the atmosphere might tend to counteract that. This is a major issue being investigated in attempts to understand the interplay of factors that determine earth temperature.

A focus on carbon dioxide has an important practical aspect. If you control the excess release of carbon dioxide due to fuel combustion, you necessarily also control the associated excess release of water vapor.

In summary, human activity ends up having much less direct influence on changes in atmospheric water vapor than it does on changes in carbon dioxide or methane. That's why the latter two gases rightfully receive more attention as controllable greenhouse gases.

The American Chemical Society also discusses this issue.