It is a communist/socialist trope that socialism entails that the workers own the means of production, i.e. "labor syndicalism". If the workers do not own the means of production, whatever it is you have, by definition it's neither communism nor socialism.
However, this definition is today nothing more than dogma inherited from the 19th century. It is no longer applicable to a post-industrial society.
First, the definition is vague. Who precisely are the workers? What precisely are the means of production? Who owns variable capital: who feeds the workers before the production of a commodity is complete?
In what sense do the workers "own" the means of production? Does each individual worker own the means of production she herself uses? What sort of ownership does a worker have over some means of production that she produces, such as a machine or a factory, when she herself does not actually use that means to produce other commodities?
When production of some commodity requires an integrated process, do the workers who participate in the process collectively or individually own the the means used in that process? What happens when a process, such as the production of a computer or an automobile, requires integrating a score of factories spread across the globe populated by tens of thousands of workers from a dozen different cultures? And, of course, our modern economy is highly integrated: almost everyone depends on almost everyone else is some way. At what point does high-level collective control of a large-scale integrated economy move from True Socialism™ to State Capitalism?
But these questions fade into triviality beside a more subtle flaw in the idea of labor syndicalism: the system of workers controlling the means of production as the sine qua non of socialism still embodies commodity relations, only the workers are now directly transforming money to commodities to more money instead of the owners of capital doing so. This is not to say that having workers having more control the means of production is a particularly bad idea; it at least eliminates the most egregious form of capitalist exploitation.
But capitalism has become a fetter on the means of production in two important senses. First, capitalism prevents increasing production efficiency (i.e. use-value produced divided by labor time) at the expense of decreasing labor efficiency (labor time used to produce commodities divided by labor time necessary to create labor power) and absolute surplus labor. If overall we produce the same amount of stuff using less labor time, there is a net loss of surplus labor and no net gain in labor efficiency; such improved productivity results in lowered profitability and cannot occur under capitalism. Second, capitalism cannot make non-commodity production profitable: to be profitable, labor must be congealed into something that can be exchanged.
Simply transferring control over commodity relations to the workers who produce commodities does not fundamentally change that commodity relations themselves have become a fetter on production.
When we talk about "ownership" we're talking about granting political status to a class based on their political and physical relationship to that which is owned. Therefore, labor syndicalism entails granting political power to the class of workers who produce commodities.
We cannot fault the 19th and early 20th century socialist and communist theoreticians. Pretty much everyone other than the bourgeoisie was either in the industrial proletariat or agricultural peasantry. Everyone was employed creating commodities: labor syndicalism (to the extent it included the agricultural peasantry) was exactly the same thing as popular democracy. The problem they had to solve was capitalism's fetters on distribution, ensuring that the proletariat received something more than bare subsistence for their labor.
But, while distribution remains a problem, our primary problem today is moving production to a post-industrial model. First, we have to improve production efficiency at the expense of labor efficiency: We must produce the same amount of stuff (or less stuff of higher quality and durability) using less labor overall, instead of producing more stuff by improving labor efficiency. Second, we must increase non-commodity production: we must produce more use-value — especially intellectual property — that cannot be easily "congealed" into commodities that can be exchanged.
Fundamentally, labor syndicalism leaves the producers of non-commodities with no political power. A computer program, for example, is fundamentally not a commodity; it cannot be exchanged without draconian copyright laws. Even though I own my means of production, that ownership confers no real political power because I cannot use my means of production to create a commodity.
I could sell my services as a computer expert instead of writing and distributing computer programs. But services are commodities only to the extent that labor power itself is a commodity: the commoditization of labor power is the distribution problem of capitalism in the first place.
Labor syndicalism makes sense only under industrial conditions, where the vast majority of people are in fact producing commodities, and producing commodities necessary for general consumption. It might be a more moral way to achieve what capitalism has achieved: maximizing labor efficiency. But labor syndicalism cannot "break through" to post-industrialism any more than capitalism can break through: in both systems political and economic power is still tied to the production of commodities.
Labor syndicalism cannot achieve true production efficiency by using less labor overall to produce the same amount of commodities. Labor syndicalism cannot achieve increased non-commodity production. Fundamentally, labor syndicalism cannot achieve the communist goal: "from each according to her abilities, to each according to her needs."
This is not to say, however, that we must continue to exploit — in an global sense — those who do in fact produce commodities. But the production of commodities cannot be driven only by the needs and desires of those who produce commodities, in the same sense that production cannot be driven only by the needs and desires of those who own capital. In some substantial sense, the ownership of the means of production of stuff must be democratized beyond the bounds of immediate production: The people, not just the workers, need to own and control the means of production. Labor syndicalism will simply not suffice for post-industrial communism.