I've heard this with trains, where a particular train on a line isn't necessarily going to stop at every station, so the passengers need to know in advance what the train is going to be doing. So this stop is X, the next stop will be Y informs people of what's happening, and also gives them a chance to get off the train if they're about to go a lot further than they wanted to!
But as well as that, it's a natural way to talk about the future. I know it might sound strange (isn't the route planned? Don't they know right now what the next stop will be?) but it's not unusual. It has a friendlier and more polite sound - you'll often hear things like the store will be closing in five minutes, versus the store is closing in five minutes which sounds much harsher and almost confrontational. Obviously the next station is [whatever] doesn't have the same sense of "so you'd better get out!!" but will be still has that professional, polite air to it.
Also, and I don't know if this actually applies to your subway specifically, you could have a fixed way of talking about stations to make things consistent and clear to riders. Always saying this station is X, the next will be Y makes it explicit that if you hear is then they're talking about the current/upcoming station, and will be means the one after that. This can be important on trains where people can only hear part of an announcement, and you don't want them to be confused about whether X is this one or the one after