I think the whole David/Dr Shaw situation is interesting and so ambiguous its open for debate...
*We see David gets a Agenda to Create for himself...
*We see there are Female Engineers....
*We see in Davids Workshop Infant Humanoid Skulls..
*We hear that David had used Engineers but the results where not as intended and it took a Human to gain David the Fruits of his Labor.
*We hear David explain that he wanted to create a New Paradise and he wanted to Evolve Dr Shaw but she refused....
It paints a interesting picture that is open for Debate... I think when looking at the End of Prometheus, the actual Crossing Prologue, how David said he felt for Dr Shaw and the Nature Boy Song for the Trailer.
I get a picture that David has Dr Shaw held up in the Juggernaught, telling her the Environment is infected and would take Months, Years to be habitable... This allows David to go about doing what he was doing.
I think Dr Shaw grew Suspicious and one time then discovers Davids Lies, and Horrors... i would assume David tries to explain to Dr Shaw and maybe Proclaims his Love for her... maybe offering her a Covenant.. where David claims they Can Start a New PARADISE...
Dr Shaw having found out she cant get her Answers.. and she has NOTHING... But David would try and suggest he and Dr Shaw can Create a New World... he can Give her the Gift of Creation...
But she rejects David and his Perverse Ideas... and tries to do a Runner and Escape... David sees Rejection from Dr Shaw, and he takes this very bad... NOW views that Dr Shaw is the same as all Humans and so David then Proceeds to capture Dr Shaw and USE her for his Experiments.
I was drawn to similar to this prior to the Trailer when the Set Leaks happened regarding his Workshop and i noticed those Human Baby Skulls which made me think DAVID managed to allow Dr Shaw to Bare Children.....
But Alas we find out Actually these are Engineer Infants... but these ideas above, i think are a picture to consider... its HOW i look at what went down.
But that Does-Not mean its actually what went down...
So i dont think David intended to Kill her, i think maybe he intended to allow her to create/give birth to Humanoids... but then David would have likely had a Agenda to use these to Evolve into his own Creation.