The flow of electrical current is possible because electrons are

Because the electrons are "free" (some of them, of course)

This means that they are not bounded to a particular molecule or particle, this means that they can "flow" along all the material, and the rules that they respect are the ones of electromagnetism (for example an electron can't flow freely, it must follow a "pattern" this is way wen you have electrical current all the electrons are flowing in the same direction)

Another answer can be: Because electrons are charged, of course, if the electrons weren't charged the electromagnetic fields would not affect them, and even if they flowed, there will not be ani electric charge.

So you need two things in order to have current, you need a charged object, and this object must be free so it can flow along with the material.