The major argument that can be made in this regard is that Haig does not deserve to be honored because he did not do anything good in World War I. It is, of course, true that he was the commander of the British Expeditionary Force in the war and it is true that the Allies won the war. But this does not mean that Haig was worthy of being honored.
Haig was, we can argue, responsible for the terrible bloodshed of the trench warfare phase of the war. It was he who commanded the British when they were ordered into battle at the Battle of the Somme in 1916. After they took terrible casualties in that battle, it was Haig who ordered a similar attack at the Battle of Passchendaele the next year. Once again, terrible numbers of casualties were suffered.
We can argue that it makes no sense to honor such a man. Instead, we should honor the common soldiers who actually did the fighting and who were killed or wounded in such numbers due to the orders of men like Haig.
In short, we can argue that the man who orders others into battle without giving them a good chance to win and to survive does not deserve the honor. It is, instead, those who suffered and sacrificed who do deserve to be honored.