This worthy sentiment is often attributed to Marx. And it's usually done so by horrified anti-communists, when they're writing in the news about stone-throwing anarchists. It's worth clarifying exactly what Marx meant.

Private property is property owned by capitalists. These people have accumulated profit by purchasing the labour power of workers i.e. employing them.

'Shouldn't we read some Marx first?'
'Quiet, Columbo's on!' - still from the forthcoming Italian film Le Brigate Rosse(Red Brigade)

The workers produce their own value - and something extra they give to the boss. Capitalists call this profit; Marx called it surplus value. The accumulated surplus value creates capital, which is held in private by the capitalist. Ergo, private property. It's unfair and exploitative. Hence Marx's claim in the Communist Manifesto, "the theory of the Communists may be summed up in the single sentence: Abolition of private property."

There are two ways to understand this:

a) directly. Bomb & arson the means of production. Some New Leftists did exactly that in the 70s e.g. various urban American urban guerrilla movements, the Red Brigades. To be fair, many of them targetted military means of production: direct civil disobedience to destroy means of warfare or kidnap military officials. I have no moral qualms with this, but I don't think it's a revolutionary strategy. Bringing the full force of the state upon you doesn't empower anyone; it does, however, run a fair risk of getting yourself killed and imprisoned. Some are still paying the price.

b) relationally. By 'private property', Marx meant this accumulated surplus value, "the system of producing and appropriating products, that is based on class antagonisms, on the exploitation of the many by the few." Destroying private property means destroying the wage labour-capital relation it expresses. Which, for most radicals, means a revolution.

Now we're into revolutionary theory: how do we organize to destroy the wage labour-capital relation (or, more Marxist-edly, the value relation?) Do we work through unions? Revolutionary parties? What are our long-term & short-term goals? Now we have to talk about ideology, convincing people, aiding and leading social struggles against the state, etc.

I mention this a) to show how a misreading of Marxist theory can have disastrous consequences, and b) how quickly Marxist theory leads to practice. That's why I like it: a concept as abstract as private property is bound up with the question of revolutionary strategy, which means history, political parties, etc.

A Marxist defence of hair care
A vital contribution to the forces of production

I also mention it because I finally got a decent hair straightener and my socialism definitely, definitely includes salon-quality hair products. As Marx says,

Communism deprives no man [sic] of the power to appropriate the products of society; all that it does is to deprive him of the power to subjugate the labour of others by means of such appropriations.

Socialism is all about the social appropriation of social labour. It's not about destroying individual property, but sharing it.

Fierce & uncompromising, yet lush & wavy - Jane Fonda in Tout Va Bien, 1972

As we can see from comparing the two stills, if you want good hair, it's vital to understand private property as a class relation, not an individual one. Otherwise your ends really suffer.