Listening to President Barack Obama's second inaugural address, I had mixed feelings. In some ways it was a good and even a great speech, an eloquent expression of the progressive tradition in American politics. At the same time, it was divisive -- more divisive than it needed to be.More than in any other speech of his I can recall, Obama made the struggle for social justice and equality the whole of his message."We do not believe that in this country freedom is reserved for the lucky, or happiness for the few," he said. "The commitments we make to each other through Medicare and Medicaid and Social Security, these things do not sap our initiative, they strengthen us. They do not make us a nation of takers; they free us to take the risks that make this country great."In a pivotal passage, he said: "We, the people, declare today that the most evident of truths -- that all of us are created equal -- is the star that guides us still; just as it guided our forebears through Seneca Falls, and Selma, and Stonewall."His vision was noble, to be sure. The United States has the progressive tradition to thank for expanding the realm of civil rights, reducing economic insecurity and leaning against the disadvantages that fall on children unlucky enough to be born into poor families.Yet there's another tradition, no less vital to the flourishing of the American project. This is the principle of individual liberty and limited government, of personal responsibility, the private sphere and reward for merit.These two sets of ideas are perpetually in tension. A meritocratic society can't be an entirely egalitarian society, and the principle of limited government recognizes that some injustices can't be corrected. The challenge of democratic politics is to balance and reconcile these equally indispensable, unavoidably contradictory ideas.The tragedy of American politics is that the parties representing these contending principles now find it impossible to see anything of value in each other's worldview. Above all, this is sad -- because both traditions are necessary for a thriving polity, and because for much of its history the American system has succeeded better than any other in honoring both principles.I'm certainly not arguing that the two parties are equally to blame for the current dysfunction in Washington. The Republican Party has moved abruptly to the right in recent years. Also, Republicans more than Democrats seem convinced that it's right to block the other side by any means necessary. If Obama finds dealing with this opposition frustrating, that's understandable. On the other hand, it goes with the job. The president is uniquely positioned -- and uniquely obliged -- to rally the country at large, and that means trying to speak to both sides of a divided nation.I heard very little of that in the president's second inaugural. In one perfunctory paragraph, he referred to American skepticism of central authority, to the fiction that all society's ills can be cured by government and to the country's insistence on hard work and personal responsibility -- before moving on to the unfinished social-justice agenda at vastly greater length.In describing these ambitions, many of which I support, he conveyed no sense of the dilemmas they will require Washington to confront. It was as though the need, say, to preserve Medicare in exactly its present form is a self-evident moral truth, admitting of no legitimate countervailing argument or principled compromise.Obama repeatedly jabbed Republicans, reminding them who just won the election. That's fine, I suppose, but almost half the country voted for the other party's candidate, and they're U.S. citizens, too. A little generosity to the losers wouldn't have cost Obama anything, but he offered none.There wasn't much respect, either. How could there be? If you cast all your policy ideas as moral imperatives, what does that say about people who disagree with you? Though frequently invoking "we, the people," he actually cast his speech at "we, 51 percent of the people," and in such a way as to underscore the division. It was just a speech, I know. Still, that was a pity.Clive Crook is a Bloomberg View columnist.