Simple. Higher tax burden = less disposable income = lower EFC. Lower tax burden = more disposable income = higher EFC.
And I’m not talking about knowing what the parents spent their money on “exactly;” I’m talking about having a general understanding of how family income and expenses (including taxes) affects need-based financial aid. OP’s statement that the majority of the family’s money goes to taxes is clearly hyperbolic, and maintaining that misconception will not serve OP well as he/she tries to understand how financial aid works.