Strong characters are important. However, if they are too strong to the point of being annoying or offensive, then the reader may not finish the story! Face it, readers usually want to relate in a positive way to the main character.
I have to admit that I’ve had a difficult time getting through a couple stories because the main character was such a piece of work I wanted to slap her upside the head. However, I also recognized what a great job the author was doing creating such a vivid, albeit abrasive, character. Thus, I pressed on, sometimes rather slowly, and finished the stories. And guess what? In both cases I gave the story five stars in my review.
Granted, not all readers will force themselves to finish a book with a character who makes them crazy, so it needs to be done with care. As an author, however, take careful note of the expertise it took to creative such a vivid character and learn from it.