Why must a person be a Christian to be good?

A person does not have to be a Christian to do good things. C S Lewis says in Mere Christianity that a person who is a Christian is not necessarily better than a person who is not a Christian, but any person who comes to Christ will be a better person than that person would be without Christ. One of the many incredible advantages to Christianity is that as long as we are admitting our failures to God, He will, through Christ and the Holy Spirit gradually (or immediately) cleanse us from the iniquities (wrong desires) that undergird our confessed failures, allowing us to grow in goodness and truth with His grace.