The market is one-dollar-one-vote. If you start with an equitable distribution of wealth, then sure, it's the will of the people. But if you start with wealth being disproportionally skewed towards a very small class - as is the case in every real-world developed economy today - the result is oligarchy, not democracy.
The problem with mainstream economic right is that it ignores that, or assumes that markets will eventually equalize naturally somehow. The problem with mainstream economic left is that it wants to strangle the market instead of freeing it from oligarchy.
Socialism is a word that can be defined in absolute terms. But left/right is defined relative to society as a whole. Whoever is left of center in political mainstream is the economic left, by definition.
The problem with mainstream economic right is that it ignores that, or assumes that markets will eventually equalize naturally somehow. The problem with mainstream economic left is that it wants to strangle the market instead of freeing it from oligarchy.