It is not impossible to become an actor. Turn on the television, go to the movies, attend the theater , and you will see people who have done it.
However, it is very, very difficult to become a professional, full-time actor. This is because there are far more people who want to be an actor than there are opportunities available. Taking acting classes helps, building a portfolio of school and community theater performances help, getting an agent helps, going to every audition you can helps, being talented helps, having good looks helps, being charismatic helps, living in Los Angeles or New York helps, but the odds are still against you.