If there is such a simple argument for physicalism, how come everybody hasn't always been a physicalist? That's a good question, and there is a good answer. The 'causal completeness of physics' wasn't widely accepted until recently.

I realize that I won't have quite enough time to understand everything - but that hasn't stopped me wanting to understand as much as I can.

I favour an interpretation of quantum mechanics (the 'Everett interpretation') according to which reality branches in any chancy quantum situation. On this view, Schrödinger's set-up will give rise to in two future branches of reality, one with a live cat, and one with a dead cat - and the talk of '50% chances' just indicates that the two branches are both equally real futures of the cat that originally entered the box.

Philosophers sometimes also use 'reductionist' more strictly, to mean 'type-identities' between mental and physical categories, and to exclude 'non-reductive physicalisms' like metaphysical functionalism.

I say that there is nothing deficient about our current theoretical grasp of mind-brain identities. The problem is only that they are counter-intuitive.

The relevant features of scientific practice often have mundane explanations which don't point to any deep metaphysical moral. (Thus it would simply be messy and pointless for the chemists to essay physical reductions, or for the biologists to offer number-free explanations. It's a weird kind of science-worship that views these practical considerations as clues to the nature of reality.)

Of course, there remains the question of why we should find mind-brain identities so persistently counter-intuitive, if they are true. But this is a simple psychological question, and there are a number of plausible explanations. Indeed this is a topic that is quite extensively discussed outside philosophy, by developmental psychologists and theorists of religion among others, under the heading of 'intuitive dualism'. It is rather shocking that so few of the many philosophers working on 'the explanatory gap' are familiar with this empirical literature.