The context was keeping the profit margin the same - but you always are the one who takes things out of context.If all businesses are reducing their prices and keeping the same profit margin, how is one particular business suppose to increase their market share? Suppose the company doesn't have profits (some companies actually lose money, ya know)? Hint: market share does not equal profits.
This point is made to tell you why the eliminated tax costs will be squeezed out of prices after the elimination of the income tax, payroll tax, and 90% of compliance costs.
When those costs are eliminated, business will enjoy a much larger profit margin. Hence, they can reduce their prices and still earn the same profit margin.
If one business sees this (and they all see it already), they can gain market share by lowering prices below their competitor's price - and still make the same profit.
How much this can be done depends on exactly the same things as today. - which is why some business is successful and others aren't.