Scrum makes the distinction between supporting the team in WHAT work they do and HOW they do it. Trying to have one person play both of these would create a great deal of conflict. How do you choose in a stressful situation between negotiating features or helping the team grow and reach consensus. A scrum master is a facilitator, how can he/she facilitate if she owns the project too?

"The Product Owner and Scrum Master roles complement each other; The Product Owner is primarily responsible for the “what” – creating the right product. The Scrum Master is primarily responsible for the “how” – using Scrum the right way. Only when the right product is created with the right process is enduring success achieved." –Roman Pichler, “Agile Product Management with Scrum”

Here is my visual view between the tradition vs. scrum roles...

http://skipstoneconsulting.blogspot.com/2011/12/identifying-with-titles-or-what-happens.html

In summary, to specifically answer "Why can't the scrum master and the project manager be the same person"? is because you can not (should not) ask one person to be responsible for HOW the team does their work and WHAT work the team does because under business pressure, the person will cave or favor one side of the spectrum. Mostly likely the "What" part. With some there watching over the "high" you ensure that quality and good team practices and more are also getting the focus that is needed to keep a healthy performing team, while the other is focused on making sure that healthy performing team is getting good focused input and vision from one source.