Can someone explain to me why interest expense is excluded from the capital budgeting process?

I understand the textbook explanation is that this is essentially double-counting, but can someone please illustrate a real-life example?

If my firm is financed 100% on debt for a total capital amount of 100, and my cost of debt is 10%, I would be paying interest of $10 every year. Let say my project generates a year 1 and year 2 free cash flow of 100,000. I would still be obligated to pay the interest of $10. But if I discount my entire 100,000 cash flow by 10% using wacc, it is saying that my debt obligation (cost of debt) would be 10,000. How does this make any sense?

I am struggling so hard on this concept.