No, you are incorrect in your reasoning. As you pay down a loan, you reduce the interest you will pay in the future. For simplicity's sake, let's assume you have two debts:
- A credit card debt of $30,000 which is charged 20% interest per year
- A mortgage loan of $300,000 which has 3% interest per year.
To keep our example simple, we'll assume that you make one payment to each loan per year and the minimum payment is just whatever interest is accrued.
Assuming you pay the minimum, you'll owe $9000/year of interest on your mortgage and $6000/year on your credit card for a total of $15,000 in interest. Now let's say beyond the interest you have another $3000/year to spend on paying down your debts. If you put that $3000 toward your credit card debt, next year (and every year in the future) you'll still have $9000 of interest on your mortgage but you'll only be charged the 20% interest on $27,000 worth of credit card debt which comes out to $5,400 on your credit card interest. You have permanently reduced your total annual interest by $600 (or 20% of the $3000 you invested in paying down your debt). Next year, if you still have the same $18,000 to pay toward your debt, you'll spend $14,400 on interest and you can reduce your credit card debt by $3600. This will continue to accelerate as you pay down your debt.
On the other hand, if you were instead to use that $3000 toward your mortgage, next year you'd reduce your total interest by only 3% of the $3000 (just $90). You'll barely be reducing your interest payments at all, so the money you spend each year will continue to go toward interest rather than paying down the principal.
Year-after-year if you keep doing this, the benefits of paying down your loans compound. If you pay down the high interest loans first, you'll save much more over time