It seems that very few people understand what constitutes valid grounds for legislating laws in this country. Restrictions on individuals are supposed to be legislated solely on the basis of protecting civil liberties. Unless an individual's actions either DIRECTLY infringe upon the rights of someone else, or they diminish the government's ability to protect civil liberties, the government should have no say. Flag burning doesn't meet either of these conditions.
A flag is a symbol, sometimes a symbolic destruction can be just as harmful as a direct one. By allowing burning of a symbol of any country would anger a lot of people. Sometimes indirect infringement of rights is not protecting civil liberties as the opposition says. Can you imagine what would happen if this law was not in place? How people would react and feel when others burnt the flag of the country they are love and are loyal too? No one should have to right to let people destroy a symbol of anything so cherished.
Saying that people would be angered by something is basically a way of saying that they consider something offensive. Labeling something as offensive is merely a way of saying "I don't like something." Not liking something is not a reason to outlaw it. Part of the reason for this is that EVERYTHING is considered offensive by someone. People could be offended by a simple statement you make. People could be offended by your beliefs. People can even be offended by the color of your skin. If we were to legislate a ban on flag burning, then logically we would have to legislate a ban on everything else (which, of course, is a practical impossibility).
I myself am a devout patriot. I am very pleased to live in the country in which I live. In many ways, it is the freest nation on Earth, particularly in terms of freedom of speech and expression. However, I believe in other ways we could be much freer. Expanding marriage rights to everyone of legal age, for instance. A ban on flag burning would merely be a step back; we would be more like other nations, and that would give us something about which to be less proud.
In terms of symbols, I personally don't believe the government should entitle rights to an inanimate, non-living object (in this case, a piece of cloth), particularly at the expense of the rights of the people. Destroying a symbol is not the same thing as harming the thing it represents; it is merely expressing disapproval of it.