I didn't like how he kept referring to regeneration as death. It isn't. It's a rebirth. Nine and Eleven welcomed the change, what was Ten's issue?
What was Ten's issue? Well, a few things. As DWF said, he really hadn't had that body/personality for too long and was pretty happy with it. Whether he realized he'd blown a regeneration in 'Journey's End' or not, he knew he was getting pretty close to the end of his twelve lives.
Another thing, I think, was that most of the other regens (and the circumstances causing them) came from out of nowhere. He couldn't avoid them, didn't have much of a chance to come to grips with it, barely had time to say goodbye (and sometimes not even that). But Ten... Ten had been given advance warning by the Ood. Like being told you've got terminal cancer, we don't know exactly how long you've got left (but it won't be long), and you won't feel a thing until the very end. That kind of knowledge can really mess with your mind.
Good points from NightOwl, but also think of Eleven's assertion that Ten had 'vanity issues'. Ten simply didn't want to go because he liked that version of himself, he was happy being him, he didn't want to become somebody else.
There is a theory out there about
why Ten was so full of himself though. Obviously Nine was not the same way - a damaged man who hated himself over what he had done in the war. But then Rose came along. She 'regenerated' him in a way - she obviously cared for him and didn't think badly of him. So when Nine became Ten, he subconsciously became an even more lovable version of that guy - better looking, dashing, friendlier. And it worked - Rose flat-out fell in love with him.
Now if Rose could love him, even after everything he'd done, why couldn't he love himself? She gave him his self-confidence back. Unfortunately at some point along the way, he began to buy his own hype. Confidence became arrogance. Even after he and Rose had been forcibly separated, he knew that this version of him - Ten - was the version that she loved. If he changed and became somebody else, that version wouldn't exist anymore and neither would Rose's love for him. That's why he didn't want to change - it would be losing Rose once and for all.
Personally I never could get into Smith's Doctor and really The Day Of The Doctor showed how similar his and Tennant's Doctor are.
In some ways they are, but they are different as well. Ten had a heroic, swashbuckling style, whereas Eleven could be a huge dork. One my favourite moments of Eleven is from "A Town Called Mercy", and it's such a tiny thing. It's when the Doctor has found Kahler-Jex's escape pod in the desert. Trying to get it to open, he starts bongo-ing on the top, then hits too hard and shakes his hand, "Ow!" That's just so adorably daft and I can't see Ten doing it at all.
The Doctor did not mean to reveal himself to Rose, she just noticed him because of his dying cramps at the wrong moment. I think their interaction was fairly harmless to the time line. She probably didn't even remember him months later when she met the Doctor proper.
Plus of course, when she did meet the Doctor again, it was a very different looking Nine. Her first look at Ten was just some random guy in the shadows, drunk on New Year's Eve.
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