Neoliberalism is a center-right, corporate capitalist economic ideology. It has nothing to do with the Left, which it sees (and is seen by as) an enemy. (Americans are particularly likely to get confused by this because the dominant, more centrist faction of the Democratic Party is neoliberal, and the Democratic Party is the left-most of the US’s major parties.)
But, yes, it has played a central role in atomization of society.