Why a fixed-rate debt’s duration will be higher than a floating-rate debt’s duration?
You’re talking about effective duration.
The effective duration of fixed-rate debt is slightly shorter than the bond’s maturity.
The effective duration of floating-rate debt is close to zero: it’s less than the time to the next reset date.
Also, just practically speaking:
If you think about duration as sensitivity to interest rate changes, a fixed rate instrument would have more duration (sensitivity) than a floating rate instrument, since the payment tied to a floating rate instrument will change with changes in interest rates.