No political good can come of it. He will either need to argue against her position logically, which will look insensitive (also he's not great at logical argument)... or, he could try to appeal to emotion.To date, he's appealed to the emotion of honoring those who are there by "upholding the mission" and "staying the course". But Sheehan has a more powerful and personal emotional appeal, so it leaves Bush without a leg to stand on.
The question that she wants answered is not one that's politically advantageous to the President. She has repeatedly asked what the "noble cause" is that the troops should stay and fight for. She's demanded a definition of the mission that we've yet to complete, and the administration has not taken a clear stance on what that mission is, especially now that the justifications for going to war have been disproven. Speaking to her would force the President to articulate a message that the administration has purposely kept vague, so the only way to avoid going on record and answering a question is not to allow it to be asked.
Plus, and this is hardly ever reported, he DID meet with her once before, in a small group of other parents. Sheehan decided not to say anything at that meeting. She had her fair chance.
Because he is not aware of the responsibilities of being the President of the US. Bush has made a long history of ignoring the obvious for his own personal gain and arrogance. When things get bad, he has historically veered away from dealing weith things and people responsibly and run home to hide under his extravagant bed. Last time the walls were caving he 'found' Jesus. But Cindy is far too complex for his thought patterns to deal with.He'll meet with Tom, wacko preachers, torturing dictators, but cannot open his presidential door to a citizen and a taxpayer.