However you could also argue that Haig is being realistic about the situation when he says “No amount of skill on the part of the higher commanders, no training, however good, on the part of the officers and men, no superiority of arms and ammunition, however great, will enable victories to be won without the sacrifice of men’s lives.” This basically says that however well trained and well equipped the men are, there will still be many losses on both sides and that they would not be able to break the enemy lines without huge casualties.
The origin of source A enhances its reliability because Haig helped plan the battle, so he would have an idea about how many casualties there would be. Also, if this was a piece of private writing it would make it more reliable because he would be less likely to lie to himself if he was the only one to read it.
Source B is different source A because in source B it sounds as if he cares more about the soldiers feelings “Men are in splendid spirit.” In source A he is more negative, basically saying that there are going to be many deaths, but in source B he is more positive “The barbed wire has never been so well cut, nor the artillery preparation so thorough.”
However, the origin of source B leads me to question its reliability because it is written by Haig for a report which he would most likely exaggerate how well it is going even if it isn’t because he might be giving the report to someone else. Also he isn’t that likely to go down to the frontlines to see what it is like himself so he may have had someone else’s report which would have made it less reliable. Plus, Haig might have made it sound really good because it was the first day of the battle and many people would want to hear of a success.
Overall I think that source does not prove that Haig does not care about the lives of his men, but that he is thinking realistically about what will happen to his man in the next days.