The simulation argument is false, but your statement about why it is false is wrong. Your argument is the following:
However, it seems to me that the argument is ridiculous. The idea is that we develop simulations that somehow "completely" capture our reality, or are at least qualitatively indistinguishable, and that we would use these simulations to map out the history of our species or something like that. Now it seems to me such ancestor simulations contradict everything we have learned about the physical world and dynamical system theory, including the inherent uncertainty of quantum mechanics, the problem of divergent paths from chaotic theory and the issue of irreducibility as laid out by for example Steven Wolfram.
Quantum mechanics (QM) is not about uncertainty. The reason commonly given for saying QM is about uncertainty is that in most experiments there is more than one possible outcome and there is no way to predict which outcome you will see. In QM muultiple versions of the same system can exist at the same time. For example, in a single particle double slit interference there is a version of the particle going through each slit. These different versions of the same particle were initially in the same state and could not be distinguished. In QM each particle exists in multiple instances all the time, sometimes those instances are distinguishable, sometimes they are not. QM predicts how the instances of a particle will be partitioned up into different versions over time and assigns a numerical quantity to each version of a particle that roughly measures how much there is of one version compared to another. The numbers saying how much there is of a given version obey the rules of probability and can be used to make decision theoretic predictions about what a rational agent should do. See
"The Beginning of Infinity" by David Deutsch, Chapter 11.
"The Fabric of Reality" by David Deutsch, Chapter 2.
Quantum systems can be simulated to any desired degree of accuracy by a universal quantum computer:
And since the world is governed on all scales by quantum mechanics, false claims to the contrary notwithstanding, all physical systems can be simulated by a universal quantum computer.
You say that it is ridiculous to suppose that a human brain can be simulated but this is not true. We don't know how to do such a simulation but the laws of physics are incompatible with the idea that it can't be simulated. Also, since computers are physical systems, one computer can simulate another and there is nested simulations are possible.
But the simulation argument is false for two reasons.
First, a universal computer can be made out of any hardware capable of performing a certain finite set of operations. It follows that if the simulation argument is true, we can never discover anything about the hardware the simulation is running on. As such, the simulation argument can't solve any problems in philosophy or physics or any other subject and it implies that the real world is incomprehensible since we can't understand how the world, i.e. - the simulator, actually works. The simulation argument is as useless and irrational as the bare assertion 'god did it.'
Second, the alleged probability of being in a simulation is pure fluff. The authors of the argument provide no explanation of how to get numbers from the simulation argument to provide such probabilities. This is a serious problem that destroys their ability to explain or predict anything. Consider the computations taking place on my computer right now. These computations may be represented redundantly by many electrons flowing round various circuits. So how do we count the number of computations? Does my computer count as one computation? But the information and the computation is represented redundantly, so why not count it as several computations?
These problems have been pointed out several times by David Deutsch, e.g. - "The Beginning of Infinity" starting around p. 467, and I haven't seen any reply from advocates of the simulation argument.