If you can, it is better in the long term, but if you're going through a tough time, struggling to make ends meet, then minimum payments might get you going an extra month, rather than getting you in the red immediately.

You should re-gander at the flow chart. I looked and noticed a "is a debt high rate? pay it off first" logic flow there.

You can't just "pay everything off", and so the above chart prioritizes things which have highest interest, as pay down aggressively first.

If you don't pay the minimum, that tends to make creditors unhappy. Paying the minimum balance stops them from "escalating" - which may mean anything from angry letters to court proceedings.

I think the idea here is that if the debt is less than 10% APY you’re better off building a emergency fund and can pay off the debts in later steps. With the emergency fund you’re less likely to find yourself in a situation where you take on more debt.

There are other steps involving overpaying debt, they just happen at different stages. They're in step 1, 4 and 8.