Political divides have a tendency of leading to false dichotomies, as the sides galvanize and rationalize. Of course so-called "centrists" are not without guilt, in that their arguments often allude to these very dichotomies either by claims of a "middle ground" or the choice of a la cart stances that affirm these dichotomies.
There is always some truth to the dichotomies, but they are greatly simplified. The problem is that ideologues use these terms in lieu of argument, and the allegedly non-ideological frame their ideas around the same assumptions.

Liberty <----->Security
It's false. For one thing some amount of security is required for even a loose sense of liberty. But obviously when carried out in different ways, security policies reduce liberty. Only some forms of liberty reduce security. A sense of freedom can also increase security by increasing the legitimacy of government and thus stabilizing the society.

Compassion <------> Responsibility
Also false. This is brought up commonly in arguments about the welfare state. The fact is that we need both, and neither necessarily subtracts from the other. Compassion, in fact, can boost personal responsibility by giving needier individuals more agency over their own lives and greater stake in society. Personal responsibility, in its truest sense, means looking at your own life- where you may have failed and where you have been helped out- which should increase our compassion as a society.

Collectivism <------> Individualism
Human beings are, by nature, both. The idea of separating these concepts stringently is itself against human nature. We all depend on one another and on ourselves. What benefits us often benefits society. What benefits society often benefits us.

Public <-------> Private
While they are separate spheres, the notion that one exists at the expense of another is purely false. Some public services increase the efficiency and effectiveness of the private sector, and a thriving private sector obviously serves the public.

Now we can look at any of these and find where they seem applicable... There are times when the private actors act detrimentally to the public sector or where the government puts inappropriate limits on private actors. Some security measures subtract from liberty. Some liberties threaten security.
But what we need to be wary of is the ideological tendency to turn these specific policy issues into general assumptions about human nature... These general assumptions fit well with polar political beliefs and seem intuitive in a nation built on bi-polar politics, but they fall apart under closer inspection.
Human nature is far more complex than any dichotomy.