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First off, I'd like to make a correction in your question. You cannot tell someone that his / her reason for not believing in God is an excuse. There is freedom of choice and I believe that you can choose not to believe in God just as Christians choose to. Jesus Christ never forced anyone to follow him nor did he force anyone to believe in God because it's your choice to do so.
To answer your question, people who don't believe in God have different reasons for their actions I'll explain.
There are people who don't believe in God based on "facts". By facts I'm talking about the notion of evolution, the big bang theory and so on. People in this category tend to be philosophical in nature and try to disprove God's existence with their facts.
Then there are the other people that don't believe in God due to their past experiences. The death of a loved one or a tragic event. Some of these people prayed to God yet their prayers weren't answered hence their disbelief.
Could they be right for not believing in God ?, I'm not God so I don't know if they are or they aren't but I know one thing for sure. As a Christian,it's written in the Bible that we should "Judge not". I believe it's best to do just that.