Although Mg2Si has been considered to be a highly promising material for low-cost thermoelectric harvest of waste heat at intermediate temperatures, the great difficulty in doping Mg2Si into an effective p-type semiconductor poses a major technical barrier against utilizing the material to realize efficient devices. Here we attempt for the first time to elaborate its significantly different responses to n- and p-type doping, through theoretical investigation of the best p-type doped system, the Ag-doped Mg2Si. Using the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional, we find that fundamentally the p-type characteristics of Ag-doped Mg2Si tend to be achieved through linear clustering between Ag and interstitial Mg (i.e. Ag-Mg-int-Ag) in the < 111 > direction in the Mg2Si lattice, via strong interactions between donor (interstitial Mg, Mg-int) and acceptor (substitutional Ag) states. Such a donor-acceptor interaction leads to lowered hole concentration, on top of the outcome that the Ag-induced hole mobility is only 10% of the electron mobility in the best n-type material, the Sn-doped Mg2Si. The current work suggests that it is rather challenging to achieve high hole conductivity in Ag-doped Mg2Si, unless native defects particularly the interstitial Mg atoms can be avoided during the synthesis stage or eliminated through subsequent equilibration treatment.