The flag is supposed to be symbolic of the best virtues of the United States ie (red for the courageous shedding of blood, blue for love of liberty, and white for the ultimate desire for peace without the oppressive hand of a dictator forcing it, or something along those lines), and so the burning of it is generally a stab at the liberal virtues of the United States.
Now, flag-burning is protected by the amendment to the Constitution protecting the freedom of speech, understood by general consensus to extend to freedom of expression so long as it does not become an actual danger to the United States citizenry (Only super-conservative reactionaries ultimately say otherwise. Conservatives have long tried to make it illegal to burn a flag. They've also tried to pass the Flag Protection Act, 18 U.S.C. 700, but flag desecration is already allowed under Texas v. Johnson in the Supreme Court due to the 1st Amendment.)
Nevertheless flag burning is generally understood as a symbolic demonstration of the denial of important liberal virtues in the face of some other perspective (typically a socialist/Leftist viewpoint) which the government simply must allow because we're supposed to be noble enough not to be threatened by mere symbolic displays. (You may have serious concerns over issues like Poverty in the USA. Even so burning a flag risks alienating people who could otherwise support you.)
Liberapedia doesn't approve of burning national flags, Patriotic people of all nations are likely to feel bad about seeing their national flag burnt. We hope this shows why Americans don't like to see their flag burnt.
Curtailing Free speech and outlawing flag burning is worse.