The CIA/Pinochet coup killed thousands, imprisoned more thousands, thousands were exiled. Besides a dictatorship, Pinochet's military government imposed extreme neo-liberal "free market" economic policies that impoverished the people and enriched the elite (and US businesses).
Seeing the kind of government it likes, Israel jumped in with arms sales to the Chilean military after the coup. It was carrying out its role as a sub-contractor and partner with the US's global system, both politically and militarily (this role has expanded greatly over the decades. Now Israel is fully integrated into the USA's military/industrial/technology/security and spying system).
"Why does the world hate us?" talking media heads intoned after September 11, 2001. Look at September 11, 1973 for an insight into this question that the house-broken US media will never figure out, not only because they are usually too obtuse to do so, but also because they are paid not to.