Fundamentally, birds are bad of conductors of electricity, and as result, the electrons keep moving in their direction and bypass the birds because the cells and tissues of the birds do not grant an easy route to these electrons. Also, electricity moves from a region of high voltage to a region of lower voltage or simply put, there should be electrical potential difference. Hence, a 60000 volts of electrical power moving through a wire will continue its journey through that single wire and bypass the bird because there is no a difference in the electrical potential between these two. However, in a scenario where the bird has parts of its body touching the ground, and parts on the electric wire, then a potential difference becomes present. Hence, the electrons would move from the wire (higher voltage) through the bird's body to the ground (lower voltage). The process whereby the electricity passes through the birds's body is termed electrocution. It can lead to the demise of the bird depending on the amount of the voltage.
Only those things are electrocuted, through which the current can flow. In this case we have a bird, so we will analyze the problem from this perspective.
For the flow of current we need a difference of potential so that a net flow of charge can be established. For this to happen, two criteria should be fulfilled:
In our case the bird fulfills neither of the criteria. The Feet of the birds (only thing touching the wire) are not sufficiently conducting. Then the feet of the bird are only touching one wire and thus the current cannot flow due to a lack of potential difference between the two feet.
Short Answer would be because the current flowing through the bird (touching only one cable) is not enough to hurt them.
Say a 10kV cable is touched by a bird. Since we know that electricity flows from negative to positive (or positive to negative) and since Air is a bad conductor of electricity due to its molecules not in continuous contact. We can say that the voltage difference between a bird and the cable is at most only 0. 10kV (cable) - Air (infitinity)
If we compare this to a human touching the high-voltage cable and the ground at the same time. The voltage difference would be 10kV(Cable) - Ground (around 0.000) = 10kV which is pretty harmful.
So as long as the bird is not touching the cable and the ground at the same time or both cables at the same time, then the bird is completely safe from any voltage difference.
Cables are usually separated into positive and negative cables, The potential for shock only exists between the different cables or between the cables and ground. As the bird is only touching one cable at a time they don't provide a path for the current. There are cases however where a birds wings will span two cables and they will get zapped.
From study of Electricity, the electric current do flows along the path of least resistance. Whne birds sit on electrical cables they don't get shocked because they are good conductor of electricity. When you check there cell and tissue both don't offer electrons and that should be the path way to the flow of electricity through them.