@purpleduck,
'Why would he plan a week with her? Why would he lie so blatantly to me?' He did those things because he's a cheating asshole who wants a relationship with you AND casual sex/other relationships on the side.
I don't know if he loves you, it's possible to betray someone and love them at the same time. It's possible to plan a life with someone, and cheat on them while you do. Hell, it's possible to secretly factor long term cheating into that life plan. It's possible to do a multitude of unbelievably cruel **** to the people you love. Sadly, loving you doesn't absolve him of his infidelities.
If you don't want to work past the cheating (totally understandable) then I'd say you should only ask him 'why?' for the sake of closure once you've processed your feelings. Don't drive yourself insane wondering what she has that you don't. The reason your boyfriend cheated is that he doesn't respect your relationship.