The screwdriver…yes, awesome bit of ‘what the hell?’ in the story line. The doctor claims to be done with it because ‘it ruins the line of a jacket’
However … He abandons the screwdriver after leaving it with Davros. He encounters Davros as a child in a war no-one-land surrounded by ‘handmines’ that can surely kill the kid. In true doctor fashion he is determent to safe the boy and throws him the screwdriver as a means to help him “just make the choice to stay alive” while the doctor stands by with the TARDIS to whisk him away to safety. Until he learns the boy’s name.
What would you do if you encountered baby Hitler? The doctor leaves baby Hitler. Abandons him to fend for himself. Aided only by the screwdriver.
Thus the doctor becomes directly responsible for the mindset that would create the Dalek, who started the time war and ended all those lives.
Wouldn't you be done with screwdrivers after all that?
(I’m sure they are returning the screwdriver soon. Because fan outrage and story line)