Mouse cursor in center

AS SA says - because that is the way the OS was designed.

But think about it: Where else should it be?

You can't put it at the right hand edge, or the bottom because it will be hard (if not impossible) to see.
Putting it at the top or left of the screen doesn't help anyone much, because there are not normally any icons or other immediately useful stuff which could be under it - the do not generally go right to the edge.

So where do you put it? Right in the middle - that has the advantage that it can be seen in both it's "pointer" form (when the "hot spot" is at the point) and in the "wait" form (when the hot spot is as near to the centre as possible.
In addition there is human psychology to consider - we tend to look at centres before we look at edges.

One note in addition and correction to the interesting explanation by OriginalGriff (Solution 2):

Most artists dealing with painting, drawing and especially photography will tell you that the viewer pays most attention for the "sweet points" located at the distance approximately of 1/3 of two edges. This is called the "1/3 rule". The center of the picture is commonly referred as the "dead center".

Sometimes, these rules are deliberately broken, but only to show some special effect. For example, one of my favorite American painter John S. Sargent depicted his friend's family with his daughter positioned along in the "dead center" of the room and the painting. He expressed his sympathy to this girl who he though suffered from the lack of attention. Look, how interesting: the center position expresses the feeling of the lack of attention. (By the way, it was my son Dmitriy who brought my attention to this interesting composition solution, as he wrote it in his school essay for his arts class.)

Another example: there is a famous scene in George Lucas's Star Wars: when Jango Fett was killed, his cloned "son" Boba Fett is shown picking up Jango's helmet. I immediately paid attention that Boba is positioned at 1/3 of the left edge of the screen, facing left. Here, another well known composition rule is deliberately broken. The rule prescribes that the character should be shown facing right, so 2/3 or more of the screen should lie ahead of the character, showing "positive motion" and the prospect for further development, a way to go. It's easy to interpret that Boba Fett is shown facing the opposite direction to express desperation and the "dead line" of the character's destiny.

If software and its UI design, as in any other art, visual composition is very important. Developing productive and attractive composition requires proper qualification.

—SA