The actual system of chemicals transported around the planet, into and out of the ground by subduction, volcanism, etc, is quite complicated and involves geology such as mountain uplifting a exposed rock weathering, bog an lake formations, positions of continents affecting flow of air and seawater, etc. etc. etc.
We really can't model it on a computer in anything more than a very simplified way, because we don't even have complete records of everything that matters going back for hundreds of millions of years.
It is very likely that there are many cause-effect relationships between CO2 and global temperatures and some work in one direction and others work in the opposite direction. Other factors, such as the rise of Central America out of the sea to separate the Atlantic and Pacific circulation patterns, plus a lot of newly exposed rock to weather in multiple parts of the globe, tipped the balance towards cold about 3 million years ago. But, the temperatures still sputtered back to "warmer" about every 50,000 years until about 900,000 years ago, when the interglacial periods started coming only about 100,000 years.
Because CO2 clearly has a warming effect when it is in the atmosphere, it obviously has some effects on the net results of all of these processes. But, we don't seem to be able to model how the weather changes produce the ice ages with enough accuracy to backcast the timing of the things that the geological record seems to indicate. So, I don't have much confidence that we can forecast climate very accurately into the future, right now.
With some people looking at any short-term cooling, or even less warming than predicted, as a reason to disregard the whole idea that the long-term net effect is warming, it seems that those people are just grasping at straws to retain their beliefs in what they want to be true.
On the other hand, the people who are worried that we are close to turning Earth into Venus need to look at what the CO2 concentration has been in the distant past.
My personal impression is that Earth's atmosphere is somewhat depleted in CO2, or at least was until we doubled its concentration with fossil fuel burning. That is one of the main reasons for the most recent cycle of ice ages. The Earth would probably still be a nice place to live at around 500 ppm, but the sea level rise would (will?) be trouble for our infrastructure and the changes in location of nice climates will force migrations that are likely to cause wars. But, so would another ice age.
We really can't expect the Earth's climate to just magically stabilize for us because we can see how it has kept changing in the past. And, we really don't know enough to actually control the climate with engineering, either. That would require models much better than we have, so far.
But, we can try to not upset the climate so much that it makes changes more rapidly. And that is where the arguments come in - how much of the current warming is caused by human activities? And, if it looks like it is naturally going to get hotter or colder than we like, should we (could we) do something to "guide" the climate in our preferred direction? That kind of environmental modification is "what humans do" in most other aspects of our environment, so it is normal to think that way. But, if we get it wrong and screw it up, we could make things worse, instead of better for ourselves.