Why do Elyot and Amanda both lie to their spouses about the reasons they should leave the hotel instead of just telling the truth?

From the moment they become aware of the presence of the other, Elyot and Amanda both realize that their new marriages are doomed. From the intense questioning that Victor and Sibyl have put them through, it is clear that Amanda and Elyot have committed to marriages with boring people (with whom they are not in love) in order to forget each other. In this act, though they are on their honeymoons, enjoying the view of the French Riviera, and hearing the music play, both Amanda and Elyot are unhappy with their spouses and the sight of each other immediately brings back the passion and love that they still share. Not only would Sibyl and Victor insist on seeing their new spouse's ex, Amanda and Elyot would be subjected to even more questions about their former marriage. In order to escape, they realize that they cannot be near one another and nor can they even think of each other.