Taken from a reddit post on the subject that I think did a good job of explaining it:

I like to link the word "private" with "privation" or "deprivation". Private property is easily identifiable by its effects on others, specifically, it's deprivation. There are hundreds of thousands of hammers. Having one doesn't deprive anyone of anything. At most only one person can use the hammer.

A house is usable by an entire family, and if I own it but don't use it myself, my ownership deprives an entire family of its use. That scales to apartment buildings pretty easily. Then there's farms where basically it's impossible for one person to do all of the work on a farm or eat all of the products of a farm, but my ownership has the effect of depriving anyone the right to work there or the right to consume its products. A factory is truly impossible for one person to use, but my ownership of it allows me to deprive everyone of its products unless they meet my price demands and also allows me to deprive everyone of use of the factory to make anything at all.

Private property entails a deprivation of society of socially necessary commodities.

In the case of a grocery store, the argument could be made that the owners of the grocery store chain are exploiting their employees with low wages, and selling the products of other owners who are exploiting their employees as well with their private property, thus justifying 'taking back' what was deprived.

On the flip side, It would be very difficult to morally justify shoplifting from a co-op grocery store that sells products from other cooperatives, as at that point no one would be being exploited.