I don't know where that simplified chart came from (Heritage? Cato?), but it is a forensic device, not an analysis. There is no notation for the 1969 CG rate increase, or the 1990 and 1993 increases or 1978 two step decrease because they do not fit the narrative. The 1981 experience does not fit either (revenues did not begin to increase until two years after the cut), and is glossed over with a vague reference to "early 80's recession". The game is an old one. Give credit for good news to whatever you are a proponent of, ignore the business cycle when it suits you, and blame the same business cycle (recessions) for inconvenient data. All sides play it. This stuff is complex, and most economists disagree with you. They might be right, maybe not. But lets not pretend that Gibson's assertions are TRUTH, based upon some think tank chart.
The CBO conclusion: Because taxpayers can choose when to realize capital gains (and losses), more gains are realized when tax rates are lower. However, over time, the increase in realizations induced by lower tax rates is not sufficient to offset the direct impact on revenues from the tax reduction itself, for two reasons. First, revenues will always increase by less than realizations following a tax cut because gains are taxed at the lower rate… Second, increases in realizations are generally much larger in the short term than in the long term because some of the additional revenues in the short term come from gains that would have been realized in later years. …
Separating the effects of changes in the tax rate from other factors affecting capital gains realizations is difficult. The best estimates of taxpayers’ response to changes in the capital gains tax rate do not suggest a large revenue increase from additional realizations of capital gains–and certainly not an increase large enough to offset the losses from a lower rate.
The Link
You may accept it as true, but it is faith, not economics that drives this particular supply side belief. it might actually be true... economic theories are notoriously difficult to prove. The preponderence of opinion disputes your position, but it is still just opinion.
Here is a serious academic effort at untangling the issue, but it is dense.http://www.brookings.edu/research/books/1999/gains