Simply put, the left wants to use government coercion to run your life as much as possible -- including purely voluntary transactions (who you buy from, how much you pay them, whether people can buy food cooked with transfats, etc.) -- while the libertarian right does not. The left thinks it knows what society should look like and which outcomes are desirable while the libertarian right has no such pretensions. The only reason there is not more of an outcry over this is because many people have made a devil's bargain with the left, by which they surrender their freedom in exchange for the lucre extracted from society's most prosperous (frequently those who are most productive).
Remember that much of leftist philosophy is based not only on the goal of eliminating need and privation (a goal the right also shares, but differs on method) but the achievement of social justice, which is simply an ordering of societal outcomes as it sees fit based on a nebulous concept of fairness that is necessarily up for individual interpretation. Social justice cannot be accomplished without Leviathan.
The decision to pursue social change through government rather than one's own individual initiative in turn leads to the absurd spectacle of politicians with zero experience in the private sector holding forth on such weighty matters as the type of energy we should consume, how our health care system should be structured, and the type of cars we should be driving. (Libertarians do not pretend to have the answer to any of this questions, and instead advocate returning freedom to the people in order to figure it out themselves. Leftist thought is implicitly arrogant while libertarianism is humble and a recognition of one's own limitations.)
Let me be clear, however, that many of those with left-wing beliefs do in fact start and fund such organizations, and for that they have my admiration. This is more directed at those who do not choose such a path and instead simply lobby for more government intervention to accomplish the social outcomes they desire. (Related points by Don Boudreaux here)
This lack of any precise definition helps explain such absurd contradictions such as leftist railing against corporations and corporate welfare, but then eagerly ladling out taxpayer dollars to favored industries such as green energy and high-speed rail. It claims to be a defender of the first amendment and against censorship, but then pushes for campus speech codes. It favors more government intervention in the economy while stopping short of communism and outright ownership of production (although health care is a notable exception), with no apparent rhyme or reason as to what the correct level of intervention is. It is given to the fancies of the moment, and whatever happens to be fashionable at a particular time. The contradictions are reconciled under the overarching rubric of "progress" (e.g. taxpayer money for solar companies may be corporate welfare, but solar power represents progress, therefore it is permissible).
- Favorable to or in accord with concepts of maximum individual freedom possible, especially as guaranteed by law and secured by governmental protection of civil liberties.
- Favoring or permitting freedom of action, especially with respect to matters of personal belief or expression.