To quote Queen, “No, no, no, no, no!”
Tom and Dingus had this same misconception, I don’t know where you guys are getting it from.
It’s stated several times in the movie that they cannot stop the plague, because it already happened. The whole point of sending Cole back into the past was to locate an original strain of the virus before it mutated in order to help create a cure, to cure it in the present so they can retake the surface of the planet. They say this so many times in the movie I don’t know how anyone could miss it. (Why having an original strain helps make a cure I don’t know, I’m not an epidemiologist.)
Furthermore, the bad guy (“Dr. Peters”, David Morse), opens the plague vial in the airport, exposing the inspector, himself, and everyone else. That’s it, guys, the plague just happened. Right there on the screen.
The scientist on the plane isn’t a younger version of the doctor from the future, that’s her, traveled back from the future to collect the original strain of the virus. She’s in Insurance. Insurance doesn’t prevent disasters, it just helps repair the damage afterward.
Really, the only thing that doesn’t make sense (to me), is why they send Jose to give Cole the gun. They know he can’t stop the plague (it already happened). So, as Dingus said in the podcast, the only thing that makes sense is that they know that, historically, Cole died in the airport that day, and they’re just “closing the loop”. But that doesn’t make much sense to me – the whole point is that they can’t change the past, no matter what they do, so why go through such machinations to “make sure” it happens “correctly”?
The only other explanation I can think of is that they’re punishing Cole for pulling out the tooth to try to prevent the scientists from pulling him back into the present. But that seems like a thin thread.
One other thing people question is, when Cole left his recording in the airport, that tells them that the 12 Monkeys didn’t do it, why don’t they get that recording until the 2035, or whatever year the present is? Well, that’s a bit of a plot contrivance, for sure, but they do say that it takes them time to reconstruct the recordings; the recording he made in the airport, and the one Katherine makes earlier, only get reconstructed when the plot requires it. The movie does explain that.