This is a very sensitive matter to discuss academically because no religion wants to have scholars saying "here's why this religion exists." Instead, people who believe in a religion tend to believe that it is true and that is why it exists (while all other religions are in some way false).
Scholars would say, though, that there are different religions because people in different areas of the world experience different conditions and have different cultures. Their religions, therefore, come to reflect this.
For example, all of the world history books I have taught from say that ancient Mesopotamia had a religion whose gods were much harsher and scarier than those of the Egyptians. They say that this was so because Mesopotamia had harsher conditions -- life was harder and so people believed in a religion with harsher gods. The MNSU.edu link says
Today, there are numerous challenges and problems faced by humans from every possible background, location and social class. Every day people must face issues of health, safety and mortality. It is because of these daily challenges that religion continues to exist. Religion is the universal tool for explaining things which we do not understand through the context the known physical world.
This sort of explanation assumes that religion comes from the needs of the people. Because people in different places and situation have different needs, different religions arise.
It is not at all a sensitive matter rather it is very easy and natural to understand that why there are different religions in the world. And i contradict the above statement in which it is said that only one religion of a certain believer is right and the rest is wrong. I state that all major religions of the world are basically true that their origin is based on true teachings of their founders(Prophets) but as the time passed their original teachings faded away and some people who followed these religions created new teachings based on their own ideas and what they thought was right.
The reason as to why there exist many religions according to Islam is that God has been sending prophets to different areas and peoples according to the needs of different times.All these prophets were true but with the passage of time these religions became corrupted. Each prophet was sent to a limited area and limited people.As Jesus was sent to Israelites.
So i think it is very easy to understand this phenomenon.