In the unhampered market, all resources would be directed by entrepreneurs who use economic calculations of profit to allocate resources into lines of production that people value more highly and economic calculations of equity to allocate investment into lines that produce goods that people value more highly. Taxes transfer control over resource away from entrepreneurs toward government officials who cannot use economic calculation to determine their use and thus, taxes detract from the efficiency of the market. The extent of the depredation of taxes on standards of living depend on the proportion of resources controlled by the state. If taxes give control of 1 percent of resources to the state, then the depredation is small. If taxes give control of 10 percent, then the depredations are larger. If 20 percent larger still and so on. Tax rates don’t matter much unless by changing them tax revenues change. So the claim of your antagonist that economic progress continued normally when tax rates where higher demonstrates that taxes are irrelevant to economic activity misses the point. If you look at the data, they show that regardless of tax rates, tax revenues stayed roughly the same. I such a case, economic theory concludes that the economy would perform roughly the same even though tax rates are higher.
Put another way, your antagonist has made a category mistake. He has conflated tax rates with tax revenues. Economic theory shows that higher tax revenues will impair economic prosperity. Tax rates, on the other hand, have little to do with it (not nothing mind you, but little.) Regardless of tax rates, tax revenues stayed roughly the same and therefore, had no differential impact on economic activity at all.