I see it this way:
"Why do you want to leave?" = indicative mood; the other person stated that he/she wants to leave, and I'm simply asking for the reason (without adding my own opinion about that statement in any way)
"Why would you want to leave?" = subjunctive mood; the other person stated that he/she wants to leave, but I don't believe taht he/she really wants that, or I'm suggesting that he/she actually shouldn't leave -- therefore the use of subjunctive mood.
If you need to change the subjunctive into past form, you need to convert it to "Why would you have wanted to leave (that day)?"