I have always been perplexed with why he gave the military to a conservative general as a socialist who was under threat, was it incompetence, an honest mistake?
It wasn't incompetence, that's for sure. In Chile we have the say "La antigüedad constituye rango" (seniority constitutes rank) which has its militaristic overview. I'll go further into this later.
Let's begin by stating that political violence involving the Army began during the Presidential elections of September 4th, 1970 in which Salvador Allende won the elections with 36.63% of the votes and a margin of around 40.000 votes against the next candidate, the ex-President Jorge Alessandri Rodríguez, representing the right wing (the Partido Nacional (PN)/National Party). Due to the little margin and under the rules of the Constitution of 1925, second rounds didn't exist (unlike today) so it was the Congress with all its members the one who had to vote and ratify wether Allende or Alessandri was the next President, something that happened before and always ended up giving the leadership to the candidate with most votes.
Before the ratification, the general Roberto Viaux who leaded a military rebellion in 1969 to increase the payment of the military, began to talk in the Ercilla magazine the possibility of a foreign military intervention to Chile due to the probability of Allende's election, or to impede him becoming the President of Chile. Truth be told, he plotted and assassinated the Commander in Chief of the Army René Schneider, this in coordination with a right wing cell of the Army, the paramilitary ultra right movement Patria y Libertad and the CIA, and was arrested because of it.
Schneider's assasination occurred in October 22nd, his dead was done in order to remove the doctrine created by himself (this kind of military personnel later began to be called constitucionalistas) for the Army which was characterized by the adherence to the constitutional order, respect for the will of the people and non-intervention in politics (opposed to the military interventionism that Chile had in the prior decades, and specially between 1925-1938). Thus removing this ideological neutrality in the Army that let Schneider publicly acknowledge Allende as the actual President after he was ratified, and making easier the opening of an opportunity to create a military coup.
Yet, the Chilean Army then in 1970 and even today it keeps the mantra "seniority constitutes rank", which means that if the leading head is dismissed (in this case, because of the dead of General Schneider), therefore the next one in line due to his seniority was General Carlos Prats, who was the second hand of Schneider and followed the same doctrine. He had to assume as Commander in Chief of the Army and he did so. Further into the future, and due to Allende's need on lowering the political violence that began to increase a lot in 1972, specifically since the trucker's strikes, he puts Carlos Prats as minister of the Interior (internal affairs, and it's basically a vicepresident; note: Prats isn't a marxist), and the heads of the Air Force, Navy and Carabineros (chilean police) into three other positions, in the beginning it worked since the trucker's strikes ended, but the political unrest and the street conflicts between people loyalist to Allende and those who opposed him increased to big rates.
After being almost publicly lynched by Allende's opposers in June 23th 1973 (Alejandrina Cox Incident), and putting down succesfully the military rebellion (and trial for the military coup) of the 1st Regiment of Infantry "Buin" and 2nd Armoured Regiment leaded by the Lieutenant Roberto Souper on the 29th (the so called "Tanquetazo" putsch), and lastly, after realizing that a considerable number of his officers were closer to be disloyal to the government because they refused to claim public allegiance to Salvador Allende on August 23th, disobeying his order, he decides to quit his govt position. Carlos Prats recommended as the next Commander in Chief of the Army the general Augusto Pinochet, his second hand, Prats believed -as written in his memoirs- that Pinochet wasn't a big intellectual but for sure he would be loyal to Allende, recommendation that Allende accepted since he trusted General Prats. That only lasted seventeen days, time in which it is stated that Pinochet joined the plotters of the military coup around September 9th, and that during the military operations of the coup (that same September 11th) he took the leadership of the Military Junta in a power move: The Army completely was needed to make the coup successful, otherwise the risk of a civil war was considered big by them, and since the Army personnel was bigger than the Navy and Air Force together, Pinochet took the complete protagonism (which later provokes conflicts with the Air Force commander, military Junta member and plotter, Gustavo Leigh).
Basically and Tl;dr: General Schneider was assasinated for being loyal, next in seniority was his second hand, Carlos Prats, and when he quit, he recommended Pinochet -his second hand-, without knowing that he was going to join the plotters.
Further readings: (Sadly, most of these books are spanish resources but I believe some authors have english books related to Allende's period or they might have their english versions)
Ps: Just today I graduated from my BA in History! Virtually due to the pandemic, haha
Edit: Grammar