I am not particularly familiar with the case of atmospheric oxygen, but I can think of two possible scenarios. The first one involves instantaneous (or rapid) competing factors. If, in the same place and at the same time, oxygen is being produced and consumed, you need to consider the net effect of the two reactions. The question becomes simply: which is faster, production or consumption? (The answer, of course, may not be as simple to find.)

The second scenario involves competing factors that involve large timescales, i.e. whose effects are delayed. Take for example a predator-prey model. If the population of prey is high, predators will thrive and their population will increase. Then, because the population of predators is high, the prey will do poorly and their population will decrease. These two statements are not counter-arguments--they both apply, and together they tend to create a cycle of increase and decrease in both populations (of course, the two populations will cycle out of phase). Sometimes (re-)production of prey is faster than consumption of prey, and sometimes it's slower. In this case, you might say that the important timescales are how often prey reproduce and how often predators reproduce (or alternatively, how long it takes newborn predators/prey to reach the age of reproduction).

As a side note, large timescales are often tied to slow transport, such as how long it takes to digest food.

In the case of atmospheric oxygen, I would not be surprised to find large timescales involving transport between the surface of the Earth and the atmosphere. The oxygen generated by plants must be transported to the atmosphere by diffusion, advection, etc., which takes time. Meanwhile, any reactions occurring in the atmosphere will only affect the surface when the products are transported back. Perhaps oxygen and carbon dioxide concentrations behave like a predator-prey model and cycle on a large timescale. Or perhaps transport is actually rapid (scenario 1) and there is a steady rate of change in concentrations.

First of all, I would tell your student that felling confused and frustrated is a part of science. They should be proud of themselves for asking questions and I hope they're not feeling discouraged!

It's true that plants absorb CO₂ during photosynthesis and release CO₂ during respiration. So the question is do plants absorb more CO₂ during photosynthesis then they release during respiration? The answer is yes, we know that plants absorb a lot more CO₂ than they release because trees are, to a large degree, made out of carbon.

Trees get some important nutrients through their roots (and of course plenty of water), but for most part trees are made of cellulose, and the carbon in that cellulose can only come from CO₂ that trees absorb during photosynthesis. Of course that carbon will get released back into the air if the tree eventually dies and rots, which is why climate scientists say that forests can sequester carbon emissions (see this link ).

Atmospheric oxygen levels are unaffected by CO₂ levels. They are two different gasses. Increased temperature will increase both photosynthesis and respiration rates, but I would not expect oxygen to change much at all. Oxygen might change if we get a huge release of methane, though, because methane oxidizes to produce more CO₂ and water vapor.

The underlying concept here is the different between “qualitative” and “quantitative.” When an argument is qualitative, it uses broad concepts to reason to a conclusion. In this case, there are reactions that put O₂ into the air, and those that take O₂ out of the air. But that information alone isn’t enough to tell you what the balance between the two is.

To understand whether the atmospheric oxygen rises, it’s important to have a quantitative argument in which you use numbers. As an oversimplified example, if 8 molecules of oxygen are put into the air for every 10 that are taken out, then the oxygen would decrease. In reality, this problem is very complicated. There are numerous sources that release oxygen into the air, and sinks that remove oxygen from the air.

Some of the factors that would need to be known are how much photosynthesis and respiration are all organisms performing, how much ozone is converted into O₂, how much fossil fuel is burned, and how much oxygen is due to volcanic eruptions.

The key point is that you can’t make any conclusions without numbers and this is true for many examples in science.

Increased CO₂ levels due to anthropogenic release of CO₂ and methane does not necessarily mean that the levels of Oxygen will change. Gasses exist as concentrations and at the global scale, CO₂ will not necessarily change O₂ levels. Oxygen levels are dropping at a very slow rate but it doesn't seem to be influenced hugely by CO₂ rise:

CO₂ increases can enhance photosynthesis and oxygen release, but this effect may be short lived for many species:

I hope these resources help.