If you do it for one, you have to do it for all. He wisely followed the Federal code, which is day of death and one day afterward for sitting members of Congress, and the next day the WH protocol staff (not the President) returned the flag to its lawful position. Then, aided by the yelling of the butthurt, POTUS had cover for raising it again due to "special circumstances." Winning!
You may recall the Queen of England went through this same dilemma and hysteria when she did not lower the flag at Buckingham Palace when Diana died, for two valid reasons of protocol—one, the flag is only run up the pole at all when the Queen is in BuckPal, but she was staying with Will and Harry in Scotland so they could deal with it; and two, Diana was divorced and no longer a member of the Royal family. Only the hysteria whipped up by the tabloids made her break tradition and lower it.
For a head of state to bend to emotion from the jump means that the same demands would be start to be made by the mob (leftists, Democrats) for every leftist's death as a way to create the false impression that lefties and their foul deeds deserve top honors, no matter how relatively inconsequential or evil their actions were in reality. As a result, those who really should be honored according to our republican constitutional traditions would be reduced to nothing special due to this media-created, emotion-driven "participation trophy" ritual carried out every time a socialist scoundrel dies.
Despite McCain, the President should have been the bigger man. But the President made and took it personal and in the end, he lost. The flag is at half staff.