Because paying down the highest-interest debt first minimizes the balance that accrues interest at the highest rate, for the same total amount paid. This is a mathematical property of compound interest, not an opinion.
Behavioral research points the same way. For example, Gal and McShane (Journal of Marketing Research, 2012) studied people working through debt with a debt settlement firm and found that closing individual debt accounts predicted whether they eventually became debt-free — consistent with the idea that quick wins help people stick with a plan. That study does not show that Snowball beats Avalanche, so if Avalanche's extra interest savings are small for your situation, Snowball's motivational boost may be worth it; if they are large, Avalanche saves real money.
Group smaller debts together, or run the calculator for your 3 largest/highest-priority debts first, then repeat for the rest once those are cleared.