Because all the simple methods would probably fail.
There are many maze-solving algorithms, check this wikipedia page: https://en.wikipedia.org/wiki/Maze_solving_algorithm Now the problems with these ones on are either the necessary time (remember, this is a race) or the lack of information in <PERSON>'s case:
* Wall following a.k.a. Right-hand-method
As the others already mentioned, the Right-hand rule doesn't always work. I would add something to this: the rule provides a sure method if, and only if all the walls are connected to the maze's boundary, thus there are no loops; or on a maze with loops if both the entrance and the exit is on the same piece of wall. (See <PERSON>'s answer.)
<PERSON> could not know if this is the case.
* Random mouse method
This is the most basic one, but the drawback is obivious. The method is randomly choosing direction at every junction, and turning back at dead-ends. After an ernomous amount of time, this will with high probability lead to the exit.
<PERSON> would still be in that maze...
* Pledge algorithm
The algorithm is an enchanced wall following with a compass: you choose a direction as zero angle, and at each turn you add the (signed) turned angle to a sum. If the sum and the current direction are both zero, leave the wall and head forward to another wall. The problem is that the method, like the wall follower one, only works if the exit is on the outer wall of the maze. (The entrance could be anywhere though.)
Again, this one requires information <PERSON> didn't have.
* <PERSON>'s algorithm
From Wikipedia:
This method requires drawing lines on the floor to mark a path, and is guaranteed to work for all mazes that have well-defined passages. A path is either unvisited, marked once or marked twice. 242
Every time a direction is chosen it is marked by drawing a line on the floor (from junction to junction). In the beginning a random direction is chosen (if there is more than one). On arriving at a junction that has not been visited before (no other marks), pick a random direction that is not marked (and mark the path). When arriving at a marked junction and if your current path is marked only once then turn around and walk back (and mark the path a second time). If this is not the case, pick the direction with the fewest marks (and mark it, as always). When you finally reach the solution, paths marked exactly once will indicate a direct way back to the start. If there is no exit, this method will take you back to the start where all paths are marked twice. In this case each path is walked down exactly twice, once in each direction.
This may be the only method that could work for sure. Drawing on the floor, however, is not so pleasable during a race... And considering the possible magical propertities of the maze, even this one could fail.
The other two methods, the Recursive and the Maze-routing are too complicated to expect <PERSON> using them. 242