"Application Mail cancelled shutdown"

The first thing I'd have you do is go to Apple Menu/About This Mac and find out what version you're actually running. If you're really on 10.0.3, then I doubt if anyone can help you wade through that mess of an OS.

 

Either force quit Mail or upgrade to the newest OS.

 

Have you quit Mail (CMD+Q)?

And you're on Mac OS X 10.6.3 I suppose, as 10.0.3 from 2001 isn't able to run on MBPs.

 

Have you tried asking it nicely?

 

Open the Activity window (Window menu, Activity). See if Mail is trying to connect, send, receive, whatever.

 

--- Post Merged, May 21, 2016 ---

I am on El Capitan, MacBook Pro (Retina, 15-inch, Early 2013), 2.7 GHz Intel Core i7
I have that issue also.
Most of the time I need to force quit mail to shut down.

 

Mail in Mavericks, for me, nearly always quits extremely quickly.

Next time you find Mail in Yosemite taking too long to quit, view the Activity window to tell what's occurring. The content within that window is often muddled but for slow quits, the content should give you a rough idea.

 

You're not the only one. I definitely see it maybe once a month and have through several OS versions, on a handful of different Macs (MBP, cMP, iMac). If it happened more often I'd get to work trying to figure it out. It's an annoyance that I just let go.

 

Command Option Escape opens a "force quit" dialog in Finder. (It's in the Apple Menu, under recent items.)
Use it on Mail.