Because nitrifying bacteria are obligate chemolithotrophs. This simply means that they must use inorganic salts as an energy source and generally cannot utilize organic materials. They must oxidize ammonia and nitrites for their energy needs and fix inorganic carbon dioxide (CO2) to fulfill their carbon requirements.
Both archaea and bacteria can participate in nitrification. Although, the issue regarding the niche differentiation between ammonium-oxidizing bacteria (AOB) and ammonium-oxidizing archaea (AOA) is still not well settled.
As Tiago have said, both archaea and bacteria participate in nitrification. In fact, in some relevant environments, ammonia-oxidizing archaea (AOA) are far more abundant than ammonia-oxidizing bacteria (AOB). These environments include the biggest biome on earth, the ocean. Therefore, as your statement is false, there is no logic explanation, unless you had in mind a particular ecosystem... Best regards.
As rightly pointed by Tiago and Ramirez, there is still a huge debate on role of AOA and AOB in respect to nitrification. There are several articles which report AOA dominates over AOB in acidic soils.
In my study, where I collected soils from a long term fertilized paddy field, AOA totally outnumbered the AOB population but studies report that dominance doesn't always correlate to the functional potential.So it gets bit complicated.
But to your question there are several reports documenting the role of AOA played in nitrification.Hope that helps.
You can refer to the attachments to get some more information.