The French anarchist Pierre-Joseph Proudhon famously wrote in his 1840 book Or, an Inquiry into the Principle of Right and of Government "Property is Theft!" John Locke countered in advance in sections 25 and 26 of his 2d Treatise on Government: “Of Civil Government” (Chapter V "Of Property") with this argument:

1. For many goods, consuming them makes them unavailable for anyone else. Economists call this "rivalry in consumption." 
2. For the many goods that are rivalrous in consumption, the moment of consumption necessarily makes them private property.
3. If everyone was prevented from consuming a good that is rivalrous in consumption, it does noone any good. 
4. Hence, private property is unavoidable if we are to enjoy the benefits of consuming rivalrous goods.  

Here are the words John Locke uses:

Whether we consider natural reason, which tells us, that men, being once born, have a right to their preservation, and consequently to meat and drink, and such other things as nature affords for their subsistence: or revelation, which gives us an account of those grants God made of the world to Adam, and to Noah, and his sons, it is very clear, that God, as king David says, Psal. cxv. 16. has given the earth to the children of men; given it to mankind in common. But this being supposed, it seems to some a very great difficulty, how any one should ever come to have a property in any thing: I will not content myself to answer, that if it be difficult to make out property upon a supposition that God gave the world to Adam, and his posterity in common, it is impossible that any man, but one universal monarch, should have any property upon a supposition, that God gave the world to Adam, and his heirs in succession, exclusive of all the rest of his posterity. But I shall endeavour to shew, how men might come to have a property in several parts of that which God gave to mankind in common, and that without any express compact of all the commoners.

God, who hath given the world to men in common, hath also given them reason to make use of it to the best advantage of life, and convenience. The earth, and all that is therein, is given to men for the support and comfort of their being. And though all the fruits it naturally produces, and beasts it feeds, belong to mankind in common, as they are produced by the spontaneous hand of nature; and nobody has originally a private dominion, exclusive of the rest of mankind, in any of them, as they are thus in their natural state: yet being given for the use of men, there must of necessity be a means to appropriate them some way or other, before they can be of any use, or at all beneficial to any particular man. The fruit, or venison, which nourishes the wild Indian, who knows no inclosure, and is still a tenant in common, must be his, and so his, i. e. a part of him, that another can no longer have any right to it, before it can do him any good for the support of his life.

Sometimes when people wish there were no private property, they are wishing that there were no scarcity—or even imagining that there wouldn't be any scarcity if evil people were not withholding the earth's bounty. This is a fantasy. 

In other cases, when people wish there were no private property, they are really saying that private property—including the distribution of rights to use the "commons"—should be more equally distributed. This is a reasonable thing to think. (Nobel prize winner Elinor Ostrom persuasively argued the use of common pool resources is almost always regulated by the community. Hence, there are private property rights involved in the use of common pool resources.)  

But literally wishing there were no private property makes little sense given the fact that for so many goods, consuming them effectively makes them private property even if they weren't before. Indeed, in the case of eating, consumption literally makes the food part of one's own body, which is private property as long as slavery is banned. 

Don't miss other John Locke posts. Links at "John Locke's State of Nature and State of War."