There is no straightforward answer to why Mussolini became Prime Minister of Italy in October 1922; there is a network of reasons. The ultimate decision to who was appointed Prime Minister was the duty of the King's. His decision was based around the fear of the civil war if he had not signed Prime Minister Facta's decree for martial law two days before Mussolini's planned 'March on Rome'. This was due to Mussolini and the Ras controlling much of Italy, emphasised by the huge mobilisation of squads in socialist areas at the end of July 1922 when the Alliance of Labour called a strike which had little support and lasted just 4 days.
The March on Rome was planned on 16th October '22 and was a clear sign of power and therefore threat to the collapsing government and King, success was hinted at by the massive rally of 40 000 fascists in Naples on the 24th. Many of the army generals were deeply involved with Fascism (which was symbolic of the governments support), leading to another main factor influencing the King, the growth of Fascist support and power. Fascism had strong appeals to many – nationalists, industrialists, the elite, the youth, braccianti and many more.
It offered a physical and ruthless resistance to the socialist threat which anyone above working class favoured, because of their trade unions and strikes etc. To many others it offered excitement and a chance at regaining national pride through unification, with its dynamic appeal of uniform and structure. Fascism eliminated their enemies with the main tactic being violence, and seemed the strong alternative to the weak government who shamed the country with their actions in the Mutilated Victory.
The government lost further support from groups such as the elite and industrialists by confirming their unwillingness to act during the Biennio Rosso. Fascist support grew whilst their opposition deteriorated; the moderates from the PPI and PSI joining with Liberals to oppose the Fascists. But with the range and magnitude of their established power and support, it seemed little could stop them except the Kings decision. Fascism also appealed to the King as it benefited him.
He was prejudiced against socialism because it resented the class system and therefore favoured a republic. Mussolini's success at eliminating socialist threats (especially in rural areas) proved the Fascist control over socialism. His powerful and persuasive speaking skills and brilliant propaganda showed how he could influence the public. They had even won over the Catholics to a certain extent because of their anti-socialist policies.
The Fascists had control of most local governments anyway, and with so much public support the king could be overthrown or there could be a civil war. There was little alternative to fascism because the government had collapsed in Feb 1922 and the PPI lead by Sturzo were split on their attitudes to Fascism. The PSI had also weakened with members leaving to join the communist party. The biggest input to why Mussolini was appointed Prime Minister was the threat of Socialism, in conjunction with a weak Liberal government.
They work antagonistically; if the government had taken a stand against socialism in the early stages (which could be put down to not rewarding the braccianti and other soldiers with land) there would be no conflict and no need for an alternative-being Fascism. In my opinion there were a number of reasons that influenced the King, but ultimately the threat of Socialism revealed the weakness of the government and created opposition parties.