Push the needle all the way through the first balloon from the end to the knot.
Now push the needle into the side of the second balloon – it pops!
Why? The rubber in the balloon consists of many long molecules that are linked together like spaghetti stuck together. These molecules are called polymers.
When these polymers are chemically attached together, it is called cross-linking.
The cross links hold the polymers together, they can even stretch but once the force pulling on the polymer is too great, the link breaks and the polymer pulls apart.
Look at the end of the balloon where the needle first went in, it looks darker than the rest of the balloon. This is because the rubber is not stretched as much as the rest of the balloon.
However the middle of the balloon is much lighter as it stretched much more.
So the tip of the knitting needle breaks some of the cross links when it is inserted into the end of the balloon and pushes aside the molecules of rubber, and slides into the balloon. But enough cross-links remain together to ensure the balloon does not burst.
There are fewer cross-links on the side of the balloon so when the knitting needle pushes through the rubber it breaks some of the cross-links but the tension on the remaining cross links is too great and the balloon bursts.