The current voting system has us picking 1 candidate out of many. By saying yes to only one person we are being forced to say no to everyone else. This does not accurately reflect our approval of each candidate and often forces us into voting for "the lesser of two evils". We are forced to vote for X to prevent Y from winning. This prevents us from expressing approval for Z, who we might prefer over X, and locks us into a 2-party system by placing a cost on voting for a third party or independent.
An Approval Voting system allows us to say yes or no to each candidate. The candidate with the most approval wins. This more accurately reflects the will of the people and enables true representation for independents and third parties without having to steal votes from a primary party.