Hmmm is it really THE very reason?

It's certainly a reason, but here's maybe why we shouldn't think it's all there is to the story. Let's take it as a given that we should uncritically accept the traditional conception of our species as the most advanced. Plenty of other creatures' languages and cooperation and writing systems are so robust and yet they don't achieve that same status. And indeed, us reaching this level of advancement happened very quickly. These seem to suggest other events led to this, beyond just what our biology happens to be.

In any case:

we became so advanced...

The traditional ways in which we think of ourselves as having progressed the most involve concepts formed by our contemporary settler-colonial world. So it thinks we should be critical of that as well. What would be so incorrect about using other metrics, like how much we produce according to ability and distribute according to need? Along that axis, we're clearly far less advanced than plenty of other groups. Instead, we consider ourselves as having progressed the most because of technological capabilities, independently of the value of their impact.

It seems plausible that while there are plenty who could have created the technological capabilities to do great atrocities as we have, only we found ourselves in the external, material conditions to develop those capabilities.