Why Draco??

[Amanda]

I've read and re-read all the Elder Wand lore but I still don't 
understand why the wand chose Draco? 

We are told over and over again a wand chooses the wizard. And in the 
case of the Elder Wand LV finds out, along with us, that killing the 
wand's former master does not automatically make you the wand's new 
master. You have to earn its allegiance. 

So just how did Draco earn the Elder Wand's allegiance from DD? By 
failing to put his whole heart in trying to kill DD back in year 6? 
By almost but failing to kill two innocents in attempting to kill DD? 
By failing to strike at DD on the top of the tower and having a true 
moment of remorse or regret?  

Throughout its history the Elder Wand gave its allegiance to its new 
Master when its old Master was defeated. Right? Or did I miss 
something?

Confused and confunded.

Mandy