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A country's flag represents its cumulative actions, such as slavery, lynching, willful ignorance of those in need, and so on.
People who haven't been exposed to these unfortuate acts firsthand or refuse to acknowledge that such things ever happened, will, of course form a diverse body of people who are angered by flagburning. There are also people who find pride in their country, and its accomplishments.
I only feel proud of America when I see the potential for the principles of the founding fathers to be realized, and not given lipservice by people too shortsighted to see that we're very far from where we should be.
Donald Byrd was dragged behind a truck and dismembered by three men who claimed to be "real Americans". This was less than a decade ago. Segregation still exists in the South. There are still many parts of the country where I have to be careful what kind of company I keep.
I can still have my car searched for nearly any reason, at any time despite not possessing a criminal record. I live in a country that fears and marginalizes me, downplays the evils of foreign and domestic manifest destiny and teeters, at times, on the verge of being an amoral hegemony.
These thoughts--and many others--enter my mind when someone burns a flag. It's easier for people to focus on anti-flagburning legislation than to donate their time to senior citizens and at-risk youth.
Let it burn.