One argument we often hear when witnessing to unbelievers is that they are a "good person", so it would be unfair for God to condemn them to Hell. Aside from the fact that they are purporting to be able to define their own standard of righteousness, we all are familiar either directly or indirectly, with the stories of people who are not saved, but who do really good things. Some of these people give vast amounts of money to the poor and needy or give of their time etc. Many times, they can appear even more compassionate and altruistic than most Christians.
So how do we explain why God would condemn the work of such people, their human righteousness, as filthy rags (Isa 64:6)? These things are good, aren't they? Why don't they please God?
The answer lies not in the act itself, but in the what the act accomplishes and the motive behind it. It should be pretty obvious that if our motives are wrong before God (or people for that matter), then it makes the act sinful and brings 0 credit to our account. So if, like the Pharisees in the Gospels, we give money to the poor so that we will be noticed doing so, we might receive the praise of men, but we obtain no credit from God, because our motives were selfish.
The harder answer to see is the one where the unbeliever truly has a heart to serve those in need and gives their life to that task, regardless of whether they are noticed or receive any recognition. Why does this not please God? God hates their "good" deeds and considers it sinful because every one of those deeds has the effect of reinforcing to that person that they do not need God, they can make it on their own. Every one of those deeds is another iron bar on the cage around them that will prevent them from acknowledging God and their utter need for Him and is therefore sinful in itself. That cage will ultimately drown them in the depths of Hell.
"The righteousness of the righteous shall not deliver him when he transgresses, and as for the wickedness of the wicked, he shall not fall by it when he turns from his wickedness, and the righteous shall not be able to live by his righteousness when he sins." - Eze 33:12