Killing isn’t the Doctor’s way, not if he can help it. He prefers to live and let live.
There are exceptions of course, there always are: Daleks, Cybermen, those for whom killing anyone not of their kind has become so ingrained into their society that allowing them to continue their wholesale slaughter of other races is intolerable. For the most part though, life is too precious, people of all kinds too marvellous and extraordinary, to rob them of their chance to see what they can become.
Evolution is a wonderful thing, except when it isn’t natural.
Professor Lazarus must die.