He is a cavalry officer, encountered in Night Watch, with a conflict of loyalties. Faced with widespread rioting in Ankh-Morpork over the price of bread, he is that rarest of things - an intelligent cavalry officer with a feeling for the welfare of, and an understanding of the motivations of, the men he commands. Because of this, his first reaction when he hears that his junior officer Ronald Rust has been relieved of his command, punched in the jaw, and locked in the brig, by mutinying Watchmen, is to give a hearty suppressed cheer that one very probable source of further class warfare is where he can provoke no further harm.
Major Mountjoy-Standfast is aware of the futility of sending cavalrymen chasing rioters down streets where they have all the advantages, overhanging eaves and shop signs can knock an unwary rider right out of the saddle, and ever-narrowing alleyways are a death-trap (at least to the horses, as many parts of Morpork would see not an agent of state repression riding at them, but several weeks' worth of meat meals once they've sorted the rider). Also, his Regiment was raised in Ankh, and like many officers before and since, he is realising how difficult it is to get soldiers to obey orders that involve going down their own streets with the intention of beating up their own families and friends in the name of social control. The desertion rate is thus rising by the hour, and now he has that disgusting but dangerous little weasel from the Cable Street Particulars to deal with, urging greater application of force on the rebels, with the unspoken threat of application of force on certain Army officers...
The Major is an officer in Lord Venturi's Medium Dragoons, a cavalry regiment whose commanding officer is Lord Venturi. He was at school with Captain Tom Wrangle of Lord Selachii's Light Infantry Regiment, and suspects that Wrangle is by far the cleverer of the two. Besides, when first encountered, he has only just been promoted to Major and his rank badges are still painfully new and shiny. He is also aware that their respective commanding officers cannot stand each other, and the ongoing feud between the Selachiis and the Venturis means they are utterly incapable of working together in any meaningful way. In any case, both Colonels are nowhere near the front: they are at a ball hosted by Lady Roberta Meserole. Which only leaves him and Tom, who have both been given the same vague and dangerous order to do as you see fit.