This is a question I hear a lot.
Is there really a single answer to such a question?
In my opinion there is not.
There are so many reasons why we leave each other. A relationship is very complex. They require every effort on the part of both to remain strong and happy.
So let's look at the most obvious reasons why they fail.

Complacency in their relationship.
When either one starts to think and act like every thing is fine in their relationship. Stops doing all those things they once did each day to make the other feel special.
They become complacent and believe they need not do this to keep the other happy any longer. This will cause very serious issues in a relationship.

Lack of intimacy or unsatisfying intimacy.
This is one of the biggest issues as to why we leave each other.
We need affection. We need to express our desires. We need intimacy.
When it is boring, unsatisfying or simply not enough it stands to reason why we start looking elsewhere to find what we cannot get at home.

Lack of communication.
This issue is one that afflicts many relationships. There is no communication between the couple. They do not take time to sit and talk to each other. Their issues go unresolved. Bitterness and resentment start to grow. They wait to long to discuss things and in this the bad feelings cause hurtful words and accusations to be cast. They argue instead of calmly discussing the issues they let linger so long.

No excitement in their lives.
Take the above 3 things and add to this a lack of excitement in a couples life. Having nothing to entice their happiness. Falling into a "routine" existence and taking no time to enjoy each other. They don't try to make the time or find ways to add excitement to their lives. They start to drift apart and begin finding excitement in another.

These are just a few things I have seen happen in a lot of the relationships of my friends, family and others. There are so many other reasons we leave each other. I am curious to read some of your thoughts.