What is the point of doing good?
I have heard that what ever we do, even if it is 'good', are just like dirty rags in God's sight. Is this true? If it is true, what is the point of trying to do good?
God created us to do good: to love Him and our neighbor as we love ourselves. The obedience to that command of God will also bring you the greatest amount of happiness. I assume you know that already by experience, don't you? Each time you do something loving, like serving your neighbour, you will experience that law of happiness. Jesus Himself has said after He washed His disciples' feet, "If ye know these things, happy are ye if ye do them." (John 13:17) So, to answer your question in reverse, the point of doing good is first, because our Maker expects this from us for He made us for that purpose. Secondly, obedience to His command does create the greatest amount of happiness for others which you will share yourself as well.
However, the sad truth is that our 'best' is core-ruptured with pride, selfishness, impure motives etc. I assume that you know that yourself as well for who doesn't read his own thoughts or gauges his own feelings after you have done something extraordinary. We crave the praise as much as the dry deserts crave for water and we gobble it up as fast as our sinks swallows down the water. So in God's eyes, Who sees every inner motive and personal reflection of even our best-looking deeds of sacrifice and service, it is completely rejected because it is sinful. He cannot accept that because He is holy and just. No matter how well we try, sin attaches itself as a leech to every good deed we done, making it guilt in God's sight. Therefore the Scriptures tell us that regarding our 'justification before God' none of our works will do anything else but charge us with more sin. The only hope is therefore in the Gospel of Jesus Christ. He is the only One who could offer to His Father and Judge works that were perfect and therefore acceptable to God. How beautiful is the name Jeremiah was inspired to give to Him, The LORD our righteousness.
Friend, have you learned to loathe your own righteousness as dirty rags? Let me direct you again to Him who said, "Come unto me, all ye that labour and are heavy laden with the realization that whatever you do will never measure up! And I will give you rest as you rest upon my obedience and my sacrifice." The Saviour Jesus Christ is pointing out to you that in Him is your hope.
But then what about the 'trying to do good?' Well, even though God doesn't need them and will never accept them because their imperfections, your neighbors still need them! Let them enjoy your good and loving deeds but never built your hopes for heaven on it!