The Laffer Curve does not claim that lowering income tax rates will always bring in more revenue. It only claims that a lower income tax rate may bring in more revenue. If the tax rates are already very low, lowering the rates may not bring in more revenue. But if the rates are too high, lowering the rates will bring in more revenue. The problem people tend to have regarding the Laffer Curve is that they confuse economics with their political considerations.
Many people have political reasons to desire high income tax rates on the earnings of the rich.
They wish to prevent the rich from earning more money, even if the resulting tax revenue is smaller than it would otherwise be, and the economy less productive than it would otherwise be. They are willing to deprive the government of revenue and deprive the economy of the productivity of the rich, all for the sake of their politics. There really is no arguing this point, as it is merely the outward manifestation of envy. The Laffer Curve does not address questions of envy and redistributionist politics. It only addresses the question of how to have the healthiest economy producing the highest income tax revenue.