> How do we know that wouldn't happen anyway
We don't know what would happen if we didn't screw ourselves, but we have some idea what will happen from what we are doing.
> How do we know that the planet getting 2C hotter is the cause, and exactly how much of the cause it is?
2C? You're being optimistic. We've past 1.5 this year. The consequences of climate change have just started: right now it's minimal (people die from natural disasters, but globally that's minimal). What we see, though, is that "bad things" (e.g. natural disasters, extreme events) are happening faster and worse than what our models predicted.
In other words, every day we observe that the consequences of us screwing the climate is worse than what we thought. Let's now think a bit about that part: the "optimistic" scenario:
* We are now heading towards 4C unless we dramatically change the way we live. 2C is already out of reach, 1.5C is already here.
* At 4C, you have a whole strip of countries around the equator that becomes unlivable for humans: it's too hot and humid, meaning that we can't regulate our temperature by sweating, meaning that we die. We are not talking a few millions refugees, we are talking billions.
* Imagine billions of people, from entire countries, deciding to move to livable territories. We're talking billions of people, with their military, moving into the lands of other billions people with their military. We have never seen that in human history, but it doesn't seem good.
* Apart from that strip of land and the 4C, in a much shorter term we are talking droughts. Imagine first world countries not having enough food for everybody.
* And last point: all of this (and more) happens in a world were the amount of oil is dangerously reaching a peak (in some places it already has: the European economy feels it since 2007 because access to oil has become harder since then). Not only it means more wars for oil, but also it means that globally we will have less oil to tackle those challenges. There is no real alternative to oil, that's just a fact: we will have less energy, whatever it is.
* Of course, in order to tackle all those challenges, we will need energy. So we will be more likely to keep using oil as much as we can, which makes it even more likely that we are going towards a world with 4C.
Last fact: the climate changes that made the dinosaurs (and countless other species) disappear happened orders of magnitude slower than what we are measuring (I'm not talking predictions, but actual measurements). So it's not completely stupid to wonder if our species (on top of the countless others that have already and will disappear in the next few decades) will disappear entirely.
And again: all that I wrote above is the optimistic prediction from our current models. And from what we measure, it's actually coming faster, harder and stronger.
You can rationalise as much as you want: if you are not alarmed, you are either uninformed or irrational.