Generally:
A leftist see evil in the existing social order and have some plan to change the existing order into different social order.

Specifically:
A leftist thinks Marxism is rational.

I will take whatever definition a Marxist wants to honestly describe how they define Marxism.

Meanwhile, I will use Wiki:

"Marxism holds that class struggle is the central element of all social change. "The history of all hitherto existing society is the history of class struggle" ( –Communist Manifesto). In the present form of society, capitalism, the two main classes are the capitalists (or bourgeoisie), who own the means of producing the necessities of life; and the workers (or proletariat) who do not own those means of production and therefore must work for the capitalists in order to survive.

Marxism holds that such a system is exploitive as well as, in the final analysis, economically irrational. Marxism aims at the overthrow of capitalism and its replacement by a classless society in which goods are produced for their usefulness not profitability; and distributed according to the principles of (at first): "from each according to their ability, to each according to their work"; and finally, in the most advanced stage: "from each according to their ability, to each according to their needs.

Since the initial formulation of the above principles by Marx in the mid 1800s, Marxism has developed and evolved in various ways. While there are many theoretical and practical differences among the various forms of Marxism, most forms of Marxism share these principles:

* an attention to the material conditions of people's lives and social relations among people
* a belief that people's consciousness of the conditions of their lives reflects these material conditions and relations
* an understanding of class in terms of differing relations of production and as a particular position within such relations
* an understanding of material conditions and social relations as historically malleable
* a view of history according to which class struggle, the evolving conflict between classes with opposing interests, structures each historical period and drives historical change
* a sympathy for the working class or proletariat
* and a belief that the ultimate interests of workers best match those of humanity in general

Two points of contention among Marxists are the degree to which they are committed to a workers' revolution as the means of achieving human emancipation and enlightenment, and the actual mechanism through which such a revolution might occur and succeed. Marxism is correctly but not exhaustively described as a variety of Socialism. Some Marxists argue that no actual state has ever fully realized Marxist principles."

So, to be a true lefty one must adhere to the doctrine of this century old religion.

If you think this is irrational, and utterly foolish then you are not a lefty.

As far as contrasting Kennedy, Nixon and Apollo.

Kennedy was a liberal and Nixon was a liberal.
Kennedy didn't consider himself a lefty, he was anti-communist.

Liberals at that time and still today favor centralized government controlling the individual states and national economy. Price controls: Federal govt setting prices for various things, would have been seen as liberal idea- and that is what Nixon did.
It's doubtful Kennedy would have supported such an idea, though politicians generally bend with the wind, so it's hard to know.

Apollo:

Apollo was a fairly successful govt program designed to get crew to the Moon and safely return them before the end of the decade.
You could say it was a showcase of what socialism can do- or was used as one. As in: "If we can send men to the moon, we can do [blank]"
It was similar to the Manhattan Project, and lot of projects done during WWII. And of course the Marshal plan was also along these lines.

There is an advantage of doing something fast, throwing money at something can be cheap.
Or if you can make something move fast, it saves money, conversely, you waste money delaying doing something in order to get the money from next year's budget.