Brian Greene: "He [Einstein] found that if you have two clocks - one stationary and the other moving - the time will lapse slower on the moving clock compared with the stationary one."
Any theoretical physicist knows that "moving clock is slow, stationary clock is fast" is non sequitur - doesn't validly follow from Einstein's 1905 postulates. The postulates, true or false, entail that
either clock is slow as judged from the other clock's frame (the valid deduction).
Why does Brian Greene avoid the valid deduction? Because "either clock is slow as judged from the other clock's frame" is an obvious absurdity. If two clocks are initially stationary and synchronized, then move towards one another and finally meet, either clock lags behind the other as judged from the other clock's frame. Einstein knew that "either clock is slow as judged from the other clock's frame" is absurd and in 1905 advanced the non sequitur: "moving clock is slow, stationary clock is fast":
Albert Einstein, On the Electrodynamics of Moving Bodies, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B." http://www.fourmilab.ch/etexts/einstein/specrel/www/
"This paper investigates an alternative possibility: that the critics were right and that the success of Einstein's theory in overcoming them was due to its strengths as an ideology rather than as a science. The clock paradox illustrates how relativity theory does indeed contain inconsistencies that make it scientifically problematic. These same inconsistencies, however, make the theory ideologically powerful...The gatekeepers of professional physics in the universities and research institutes are disinclined to support or employ anyone who raises problems over the elementary inconsistencies of relativity. A winnowing out process has made it very difficult for critics of Einstein to achieve or maintain professional status. Relativists are then able to use the argument of authority to discredit these critics. Were relativists to admit that Einstein may have made a series of elementary logical errors, they would be faced with the embarrassing question of why this had not been noticed earlier. Under these circumstances the marginalisation of antirelativists, unjustified on scientific grounds, is eminently justifiable on grounds of realpolitik. Supporters of relativity theory have protected both the theory and their own reputations by shutting their opponents out of professional discourse...The triumph of relativity theory represents the triumph of ideology not only in the profession of physics bur also in the philosophy of science." Peter Hayes, The Ideology of Relativity: The Case of the Clock Paradox https://tandfonline.com/doi/abs/10.1080/02691720902741399