I do not believe that people are afraid to help others, nor do I believe that people do not want to, or are unable to help others. Most people are generally kind natured, and more than happy to lend a hand. Of course, not everyone is as altruistic by nature. Altruism is the selfless concern for the welfare of others. If you are very altruistic, you tend to help people, because you care what happens to them regardless of how it might affect you personally.
There are many other reasons to help others besides altruism. For example, you could help people because you expect them or want them to help you in the future. You could help someone because you think you have the social responsibility to help them. Alternatively, you could help because you might feel that it is simply the right thing to do. When people do not help others, this does not mean they are afraid to or unwilling to help, but often it is simply the case that people are not aware that their help is really needed.
Sometimes people do not help others, because they are convinced that someone else will help the person in need instead, and they do not have to get involved. This situation is most likely to occur when there is an emergency situation. Even in any kind of event in which someone needs help in a crowd, or when there are more than one or two standers by, people have the tendency to just stand around and do nothing. This phenomenon is also known as the bystander effect.
When there are others present, people tend to feel less responsible to provide assistance, or they might think they are less qualified to help than others are. In the worst-case scenario, this could mean that something bad happens, and the people in the crowd all just stand there and watch with no one doing anything to help. One effective way to counter the bystander effect is by simply appealing to someone personally to help. For example, by looking or pointing at a person and telling them to call the police or an ambulance.
Of course, there is a difference between every day helping behavior, like holding the door for someone or doing a favor for a colleague, and helping out a stranger in an emergency. In the latter situation the helping behavior is much more important than in the former, however, it is also much more effortful. If fear places any role at all in willingness to help others, I could understand if it comes into play in helping others in an emergency. In that case, it is not so much the fear of helping others, but the fear to put oneself at risk. Most people prefer to keep themselves safe, and who can blame them really. It takes a special kind of person to risk their safety to help someone else.
