I think a little research would answer your questions.
Gaddafi (see his Wikipedia entry) has been in charge of Libya since a military coup in 1969.
He was not elected at that time, and has not put himself up for election since.
He has ruled with oppression, terrorism and an "iron fist".
So I think the people of his country have a right to protest.
Think back to when we in the UK had Kings and Queens who had total power.
We had our fair share of wars and uprisings and killings, and even had a major civil war, before the role of the royal family and government was sorted out.
The people in those countries just want the same rights.