Why did thomas paine's common sense inspire colonists?

It made them realize Britain we abusing its power and was to ignorant of their problems to govern them

The pamphlet was written in a literary style that everyone could understand. It focused blame for the problems of the colonies directly on the reigning British monarch, George III. 

The pamphlet was in five parts; the first four contained "political theory" that appealed to educated people in the 18th century. The final part contained his observations against British rule of the American colonies. He can be summarised like this: 

1. It is nonsense for an island to rule a continent. 
2. America was not just a "British nation"; it contained influences, cultures and people from all over Europe. 
3. If Britain were the "mother country" of America, then her actions were all the more reprehensible, for no mother would treat her children so brutally. 
4. Being a part of Britain would drag America into European wars that would cause conflict within the different communities in America. 
5. Being part of Britain would hold back the commercial development of America and keep it from the international trade in which it already excelled. 
6. The distance between the two nations made governing the colonies from Westminster impracticable. Petitions sent to Parliament would take a year before colonists received a response. 
7. The New World was colonised during the Protestant Reformation and English Puritans believed that God wanted them to have a place for themselves, safe from the persecution of British rule which kept changing its attitude towards them 
8. Britain ruled American colonies for British benefit, and did not consider the interests of the colonists who created wealth and trade opportunities for British industry. 

This is the "common sense" part of the pamphlet and it appealed very strongly to many populists and amateur lawyers; though not all by any means. These days, we would regard this journalistic approach as "rabble rousing." It is the sort of thing you hear in Cuba, Venezuela, Palestine, North Korea. If Hawaiians or Puerto Ricans sought independence through this level of argument, they'd be told where to go.