Why turn-on speed of a MOSFET is linked to diode reverse recovery time
My question is why the turn on speed is linked to the diode reverse recovery time ?


It isn't. What they are saying is: usually the FET can turn on faster than the diode can turn off, however that results in both the FET and the diode being on simultaneously, ie cross-conduction, and increased losses. So it is more efficient to switch the FET a bit slower to make sure it turns on right as the diode turns off.

So a better way to put it would be "The optimal MOSFET turn-on time for highest efficiency is linked to the diode recovery time". It isn't a characteristic of the FET, it is a design choice.