He does want to go.
They’ve already more or less ruled out allowing him to serve in combat (his brother, as the “spare” is a combat soldier, the heir therefore cannot be - maintaining the succession is considered important), and so he went into S&R in the hope of actually being able to have a genuinely useful military career in a non-combat role. Now the government is raising blocks to that.
Like any junior officer, he must obey orders - he does so, but he doesn’t have to like it.
Prince Andrew deployed to the Falklands in the summer of 1982, and Queenie let him go (but, then again, he wasn’t the Heir to the Throne...)