First off, let's just clear out everyone who hasn't seen "The End of Time", the two-part final adventure of the Tenth Doctor. Please exit the post in an orderly fashion to your left. (It is important that you turn left when leaving the post. Turning right will lead to the eventual victory of the Daleks and the destruction of the universe itself.) (Oh, and um, if you also need spoiler warnings for the Season Four episode, "Turn Left", please ignore the previous parenthetical comment.)
So right, wittering on for a moment to clear out the spoiler space nicely. I do think that Doctor Who fans are the luckiest sci-fi fans in the universe. Other science-fiction fans have to grit their teeth as their favorite show enters a long, slow decline, with the people both in front of and behind the camera gradually running out of ideas and losing their passion for the show. All these Trek, Buffy, and BSG fans can hope for is that their show will die a merciful death before it embarrasses itself, and that some ten years down the line it will be rebooted by a new creator who gets it right again.
But with Doctor Who, the regeneration is built right into the series. Change is an essential element of the show. It changes actors, characters, writers, directors, producers, genres...Doctor Who, above all other shows, is constantly reinventing itself. It's always fresh. Roll on Steven Moffat and Matt Smith, I say. And they, too, shall pass someday. It's part of the glory of Doctor Who.
So that's philosophy out of the way...now, let's get on to my fanwanky theories about "The End of Time"!
Any fan who followed the Doctor during that long, strange, wonderful period when he was off the TV airwaves and ran as a series of novels (The New Adventures, published by Virgin, and the Eighth Doctor Adventures, published by the BBC) cringed when they saw the flashbacks to the Master as a little boy, staring into the Untempered Schism. This is because it's been very definitively established by the books that the Time Lords were incapable of having children; instead, they "bred" through devices known as Looms. These machines stored the entire Gallifreyan genome, and "wove" it into genetic patterns that then created Time Lords cell by cell, before pushing them out as fully grown adults. (In a charming bit of worldbuilding, Time Lord nurseries have oversized furniture to give the young Time Lords a feeling of being small.) So a ten-year old Master should be impossible.
But, I say, there is a loophole. The actions of the Doctor in "Lungbarrow" (well, technically the actions of Leela sometime before "Lungbarrow", and the actions of the Doctor in bringing Leela to Gallifrey in "The Invasion of Time") restored the Time Lords' ability to breed naturally. Meaning that if the Master was born after "Lungbarrow", he could be a child.
"But wait," you say. "Surely the Master and the Doctor grew up together?"
They did...the first time. Remember, at the end of the TV movie, the Master is reduced to an ectoplasmic body-hopping entity that's then sucked into a black hole. Not a whole lot for the Time Lords to work with when they "recreated" him as a weapon in the Time Wars. So my theory is that the Time Lords, unable to restore his old body, decanted his essence into an infant (donated by some extremely patriotic Time Lord family, one presumes.) That infant possessed...or more accurately, was possessed by...all the memories and knowledge of the original Master.
And then, at age ten, he looked into the Untempered Schism. And heard the sound of drums. Which drove him even madder than he was before (and that's hard to do) and forced him to flee to the very end of the universe itself and erase his own memories to escape it.
It explains a lot. It explains why the Master could be a Time Lord child, when there aren't any according to the books. (Those of you who insist that the books aren't canon can happily turn right.) It explains why the classic series' Master never once mention the drumbeat, but the new series' Master can't freaking shut up about it. (Sorry, editorializing there.) And it provides a stronger reason for the Master up and running from the Time War, beyond just, "Ooh, it's a bit scary."
Whaddya think, sirs?