Some say displaying the Confederate flag represents pride of heritage, but may not entirely represent an endorsement of what that heritage entails. I reject this position. Displaying the Confederate flag, as any emblem, is not an endorsement of those who were involved, but the principles they represented.

A flag is inherently a political symbol. A symbol stands in place of a set of ideas, in this case, state identification. State identification provides a set of values and rules espoused by that state. To display the flag is an endorsement of those values, if one does not support the overall actions of a state, one should not display its flag. Thus to display the Confederate flag is not a definition of a populace, in this case, your ancestors, but an enforcement of a set of values.

Which brings us to the values represented in the Confederate flag. I'll spare us all a history lesson, as most of us know the history of the American Civil War, and if you don't, there are nodes that can explain it better than I could.

So let's look at the values espoused in the Confederate flag. I prefer, whenever possible, to go to a direct source. So have a look at Mississippi's Declaration of Secession. It clearly states that Mississippi fought for slavery. From 1861 to roughly 1865, Mississippi flew the Confederate flag because of the reasons outlined in that document. Most other secession documents are similar. South Carolina's can be found at: http://alpha.furman.edu/~benson/docs/decl-sc.htm . And yes, there's more, right here: http://americancivilwar.com/documents/ . Some clear exerpts:

"For the last ten years we have had numerous and serious causes of complaint against our non-slave-holding confederate States with reference to the subject of African slavery."
--The start of Georgia's declaration.

"They demand the abolition of negro slavery throughout the confederacy, the recognition of political equality between the white and negro races, and avow their determination to press on their crusade against us, so long as a negro slave remains in these States." (emphasis mine)
--Texas' Declaration

"Our position is thoroughly identified with the institution of slavery..."
--Mississippi's Declaration

I think I've adequately proved that the Confederate flag, at least originally, stood for slaveholding ideals. I now intend to show that southern slavery as espoused by the Confederate flag was inherently racist.

It's right there in the declarations.

"(The North) advocates negro equality, socially and politically..."
--Mississippi's Declaration

"For the last ten years we have had numerous and serious causes of complaint against our non-slave-holding confederate States with reference to the subject of African slavery." (emphasis mine) (Yes, I did reuse the quote.)
--The start of Georgia's declaration.

And ladies and gentlemen, the kicker:

" (Slavery's) labor supplies the product which constitutes by far the largest and most important portions of commerce of the earth. These products are peculiar to the climate verging on the tropical regions, and by an imperious law of nature, none but the black race can bear exposure to the tropical sun. These products have become necessities of the world, and a blow at slavery is a blow at commerce and civilization."
--Mississippi's Declaration

Not only is this blatantly racist on its face, it also implies that Africans are not part of "commerce and civilization."

So, if you really feel that the symbol for your heritage should be a Confederate flag, wear it, but not with pride, for to wear it with pride is be to advocate what it represents. If it is an accurate representation of your ancestry, which I hold it cannot be, wear it in shame, acknowledge your ignorance and refuse to wear it, or recognize your inherent racism.

I have said that the Confederate flag is an illogical symbol of any heritage. Heritage is family history and a record of one's ancestors. Thus, there are two possibilities for using the Confederate flag as a symbol of one's heritage. Also, please note that using a symbol for one's heritage does not mean that one must be proud of that heritage. All that I have said above still holds, even if possibility A applies.
A. A significant portion of one's ancestors lived under the Confederate States of America.
B. Support of the values of the Confederate flag.
Possibility A makes little sense as the Confederate states lasted just over four years. That's a mighty short time to define generation after generation of one's family. Possibility B has already been addressed.

Also, because the comparison was brought up on another node, I feel the need to point out differences between the symbolism of a picture of Malcolm X and the Confederate flag. The Confederacy advocated preservation of the Status Quo at all costs. Malcolm X advocated radical change to the Status Quo. The Confederacy sought to hold those of African heritage in slavery. The legacy of slavery caused cultural damage to the African community. Malcolm X sought to change this by saying that the system was unfair and improvements had to be internal, from within the African-American community. His reforms were targeted towards self-improvement. The Confederate system called for African subjugation, the subjugation of the other. That Africans were considered other at the time is evident in that they were not considered in “...civilization.” as above.

A less philosophical argument would point to the fact that the Civil War killed hundreds of thousands, and Malcolm X saved thousands from inner-city ghettos.

Note: I mean state here in the International Relations sense of the word, not the common usage in the United States suggesting regional division.