It's called Democracy. If you don't understand Democracy, you should Google it; or perhaps you could simply brush up on your 4th grade political science studies.
No one is "born with a right" to govern. They are elected by the people to hold that right, or appointed by someone who was elected by a democratic process.
Oh dear, you appear to be favoring rationalization and fairy tales you learned in government schools over logic.
If nobody is born with a right to govern, then it is impossible to delegate that nonexistent right. That is self evident.
You have the right to appoint a leader over yourself, because you own your self. It is also consistent with the one thing you said above which makes sense, "No one is "born with a right" to govern" . In your quote it is implied "to govern others", we all have the right to self govern.
Therefore you can only delegate YOUR right to be governed, if you chose it. You cannot delegate another persons right to be free from
being governed without doing the impossible.
A democracy composed of a group of people, none of whom have a given right can no more delegate that nonexistent right than an individual who doesn't possess that given right can. An aggregate of zeroes or a single zero is still zero.
I bet you can't refute what I just said....because it's impossible.
Do I have to get my friend Lysander Spooner to appear and straighten you out ?