This is a non conditional instability. It does not depend neither on external pertubations, nor on fluid properties. After a while instabilities appear and create pressure difference between inside and outside the jet. This difference tends to increase (refer to the schematics) and the jet breaks into drops.

This instability is only due to interface tension between the two fluids and to the static pressure. Indeed Laplace's law is :

where :

Comments of Laplace's law :

As you can see, the smaller R is, the bigger the pressure difference is. Furthermore, the pressure acts so that to decrease the curving radius.

So the instability grows untill the jet breaks.