Why do I still owe interest right after making a big payment on my card?

Two common reasons. First, that interest was 'residual' or 'trailing' interest: it accrued daily on your balance between your statement closing date and the day your payment posted. So even paying the full statement balance can leave a small interest charge for those in-between days, which shows up on the next statement. Paying that too clears it.

Second, if you'd been carrying a balance, you may have lost your grace period, meaning new purchases accrue interest from the purchase date until you pay the full balance for a couple of cycles. A big payment reduces the balance but interest keeps accruing on what's left daily. To fully stop it, pay the entire current balance, then pay in full again next cycle to reinstate the grace period.