Maximize profits by offering multiple platform options. THAT'LL NEVER WORK.
It's not as simple as that. When you're Microsoft and have two separate platforms to target, there's more to think than just the profits of individual games. For better or worse, some people are going to buy the XBO for Halo. In fact, I know a few people IRL who said that they're going to get the system (at least eventually) just for Halo. Be that dumb or not, it's not the point. It happens.
So, if Microsoft releases Halo for PC, then those people who might have bought an XBO for Halo might not get one. If that's a significant number, then that means 3rd parties are less likely to release games on the XBO due to fears of their games not selling enough to justify the efforts. Then the XBO starts getting stuck in this downward spiral (the same sort of spiral Nintendo consoles get in) that lead to failure, only MS doesn't have the 1st party titles to keep the XBO afloat like Nintendo does.
So yeah, if they make a PC version, they'd be maximizing short term profits. However, the long term effects could be devastating.
That being said, if the XBO does poorly anyway (it most likely won't), causing the next Halo game to do well, they'll probably release it on the PC to help recuperate some of their losses.