You have 3 choices: an airplane, a drone, or another balloon.
Airplanes are fast, you can't just approach, slow down, reach out and poke the balloon.
Drones don't fly that high up. On the internet you can find that drones can fly as high as 33000 feet. It's likely the military has drones that fly higher, maybe even as high as this balloon. But you need one that flies that high, and also has the capability to puncture a balloon. It looks like such a modification was not doable in the given window of time.
Another balloon. That would obviously be doable. If a balloon can fly at 60000 feet, another one can too. But again, you need the modifications to make it go up there and shoot at another balloon. Maybe in the future they'll make this type of balloons, but for now they didn't have one handy. And if they had, they didn't want to tip their hand. Better to use weaponry that's widely known to exist, rather than new and classified stuff.
At high altitude these sorts of balloons are massively stretched out due to the low atmospheric pressure. A puncture will cause catastrophic failure of the balloon.
> A runaway weather balloon floating toward Britain over the North Atlantic is proving a tough target for some of Canada’s top guns. The helium-filled balloon, a 25-story high unmanned research station used to measure ozone levels over Canada, was launched Monday from Vanscoy, Saskatchewan.
> Jet fighters trying to bring the balloon down fired more than 1,000 rounds into it Thursday, but it remained aloft. The air force hopes the now-leaking balloon will eventually come down.
