They are false converts.
Jesus said, "You will receive power when the Holy Spirit has come upon you, and you will be my witnesses in Jerusalem and in all Judea and Samaria, and to the end of the earth." Some professing Christians aren't sharing their faith because they aren't possessing Christians. They haven't received the Holy Spirit that dwells inside every true follower of Christ. This is foundational. The question I would ask is this, if you aren't witnessing, perhaps it's because you have nothing to witness about? Jesus told us that there will be MANY on that day who will say 'Lord, Lord' and he will say depart from me, I never knew you.
"Have you no desire to see others saved, then you're not saved yourself. Be sure of that."
"If you don't talk about Jesus, then maybe you don't love Him half as much as you think you do (if at all)."
"If you are not concerned about your neighbor's salvation, then I am concerned for yours."
Do you believe Jesus when he says - "I am the way, the truth, and the life. No one comes to the Father except through me."
Is that true for the Muslim?
Is that true for the Buddhist?
Those who say Jesus is simply a prophet?
Or a created being?
Or one of many gods?
Does theology even matter?
What about that unbelieving friend you have who lives a really moral life? Worldly speaking, they are a good person. They try to do the right thing. They're not perfect, but they don't cheat on their boyfriend or girlfriend, they're nice to other people, and they will even say nice things about Jesus, they're just not born again. What's going to happen to that person?
Do we believe Jesus when he spoke of the reality of Hell? Many people don't believe in eternal punishment. This is one doctrine that people would just as soon not talk about. It is the doctrine people try to forget. We don't want to think about a soul being in hell for eternity.
Are the only verses that we have underlined in our Bible the ones that comfort us and make us feel good? Do we neglect those passages that grieve us, and would therefore motivate us to go and talk to someone about the forgiveness offered only through Christ.
Simply ask yourself - "If I'm not sharing my faith, is it true that when it comes right down to it, I really don't believe what God has said?"
We lack compassion
Many believers are like Jonah. Jonah did not want to warn the wicked! He didn't care for the people of Nineveh. He wanted to see them perish! In fact, that was the very reason he ran from God (Jonah 4:2). We need to repent of our calloused and hard heart. We're unwilling to suffer rejection from the world for the gospel's sake!
The expression about the Bible, applies to evangelism as well... Sin will keep you from sharing your faith, and sharing your faith will keep you from sin. You'll feel like a total hypocrite.
We're too busy
Churches organize all types of efforts related to fellowship such as children's events, parades, cook-outs, ball teams, and other events while completely ignoring the great task of evangelism. Often the church finds itself focused on entertainment or good deeds without the gospel.
"Oh my friends, we are loaded with countless church activities, while the real work of the church, that of evangelizing and winning the lost, is almost entirely neglected."
Oswald J. Smith
The biggest reason is...
"We overcome our fears through love. The Bible says that perfect love casts out all fear. Think of a firefighter. He's up a sixty-foot ladder. In front of him are a mother and two children, clinging to each other in a window on the fourth floor of a burning building. Flames are licking at the terrified family. If he doesn't rescue them, they will certainly die. Would he rather be home spending time with his wife and kids? Of course he would. But he ignores his fears and he denies himself his own legitimate pleasures because he is thinking of that family's terrible fate. Love consumes his fears." Ray Comfort
A convicting thought... If I said to you, "I'll pay you $1,000 every time you shared the gospel, then how many times would you share your faith today?" If you would do it for money, how much more should you do it out of love for others and gratitude to God for what Christ has done for you?