Fixed income - Structural model: why is holding debt equivalent being short a European and not an Amercican put

Hi! In the structural model option analogy, holding debt is equivalent to being long a bond of the value of the debt, and short a EUROPEAN put option with strike price K. Why is it not an American option? American options can be exercised at any time, while european one can onely be exericised at the end. So the asset owner could exercise it when a default occurs?

Thank you!

I think because the debt of the firm can not be repaid before its maturity date.

If the firm holds a american puttable debt, holding this debt will be equivalent being short american call.