A straw centrist is a person who always takes the middle position on issues. For example, if you asked them if we should kill all the men or not, they would say that we should kill half of the men. If you asked them if we should kill all the women or not, they would say that we should kill half of the women. And if you asked them if we should kill all the children or not, they would say that we should kill half of the children.
But it wouldn’t just be disjoint groups for which this is true. If you asked them if we should kill all the teachers or not, they would say that we should kill half of them. But how could they make sure that they don’t accidentally kill over half of the teachers while killing half of the women? Well, by the law of large numbers, there is a really simple method to ensure that they kill half of every group: choose a random sample to kill. If the sample size is equal to the size of half of the population, then they will achieve all of their goals at the same time.
Now we see how Thanos qualifies as a straw centrist: his plan is exactly what we’d expect from one. This also explains why he talks about balance all the time. A straw centrist picks the middle position on every issue because they want to balance the advantages and disadvantages of each side. In the same way, Thanos kills half the population because he wants to balance the advantages and disadvantages of killing everyone and killing no one. Therefore, it’s safe to conclude that Thanos is indeed a straw centrist.