Mussolini's political leanings can be debated heavily and were never really clear. Some called him an Anarchist, sometimes he rejected that label, other times he wore it with pride. Its fair to say like most youth, Mussolini jumped from party to party, from political leaning to political leaning. By around 1902 Mussolini was moving towards Socialism. Now Mussolini eventually fled to Switzerland to avoid creditors and military service. There he met influential socialist, Angelica Balabanoff, who introduced him to the "classical" socialists like Marx, and Sorel. Now it would later be denied by both communists and fascists alike, but for a period of about 10 years, Mussolini identified as a hardcore Marxist. He began to spread unrest among Swiss workers in the place where he lived and thus the Swiss gave him back to the Italians. He again fled to Switzerland in 1904 to avoid conscription. During his second stay in Switzerland he began to develop a strong atheist leaning and would shock crowds with his inflammatory statements about religion.

He eventually was forced to Join the Italian army, in the army he began to tone down his revolutionary Socialism. Eventually, he left the army and began to bounce around from various political leanings. Angelica Balabanoff said this:

his views were more the reflection of his early environment and his own rebellious and his own rebellious egoism than the product of understanding and conviction

He eventually fell back into revolutionary socialism and bounced around Austria and Germany until the first world war started. After the war Mussolini displayed his ability to play both sides, he openly talked up the aristocratic classes, but also pandered to the socialists. Mussolini wanted to establish a populist dictatorship, and the "fascist" movement as he called it, didn't really have a clear doctrine and it was designed to pander to anyone. The main difference between Fascism and Socialism, as Mussolini put it was that Fascism would preserve social liberty for all. Here is what Mussolini wrote:

We are libertarians above all else, loving liberty for everyone, even for our enemies.

The change from left to right came when Mussolini failed to win many seats in the 1919 election. The parliament of Italy was fractured and the only significant party was the Socialists. This scared the conservatives who began to support Mussolini. Mussolini figured since fascism hadn't gone over well with the left, he might as well try the right.

So to get back to the original question, Mussolini started as a very left leaning person that bounced around from ideology to ideology. But when he saw what opportunities the right wing offered him, he jumped at the chance, and his fascist party went with him. They changed from a socialist party committed to freedom, to a right wing, party that used paramilitary forces to gather support.

Sources:

Mussolini by Dennis Smith

The fall of Mussolini, Italy, Italians, and the Second World War by Philip Morgan