Before the incestuous events with the daughters occurred, the family experienced some awesome and heartbreaking events in a very short period of time. They had to run from Sodom (no doubt leaving virtually all their possession behind) in order to save themselves. They then saw the aftermath of Sodom and Gomorrah TOTALLY destroyed and wiped completely from the face of the earth. Then, not only is Lot's wife turned into salt, they must flee yet again out of fear and end up living in a cave. Would any of us not feel a bit distressed, uptight, confused and afraid of what might happen next if we saw and experienced what they did?
It certainly seems the daughters panicked when they were at the cave with their father. This may have led to their confused thinking, which led them to make conclusions that were not accurate, which were then used to justify their over-reaction to the situation.
Consider the following. The Bible states the daughters felt they had to do what they did because they believed NO MEN were left alive (Genesis 19:31), certainly in the area they were in if not the WHOLE WORLD! But was this REALLY true? Before they ended up in a cave the family stayed in Zoar for a short period. Though small, surely there were at least a FEW men who lived in the small village! It seems rather unlikely the city was composed of ONLY females and maybe a few boys too young to produce children. Some may counter that, no matter who lived in Zoar, the city was also destroyed when God took care of Sodom and Gomorrah. Therefore, for all the two daughters knew, all men (in the world?) were dead when they reached the cave. Several Bible commentaries even go so far as to state Lot left Zoar out of fear it would also be annihilated. This reasoning, however, is nonsense!
Zoar survived what happened to the two disobedient cities. How do we know this? First, the two angels who saved Lot not only allowed him to flee to Zoar they PROMISED (remember, they are representing God's will) the city would NOT be destroyed (Genesis 19:21). Second, the Bible records that it was AFTER God completed the destruction of the cities (see again verses 24 - 29) that the family left Zoar. If this is true, then why did Lot leave the city he BEGGED to go to? Though the Bible does not give us a reason, could it be he feared for the safety of his two young virginal daughters? Could it be he feared the MEN of the village might try to ravage his daughters and put them in the same danger they were in at Sodom (Genesis 19:1 - 9)?
The daughters' desire to continue the human race after Sodom and Gomorrah (and believing all men were dead) is certainly noble, but they went about it the wrong way. Their behavior appears to be based far more on their skewed thinking brought on by fear and panic than anything else. As for Lot, he sinned willingly, but not willfully. He succumbed to his human nature (as we all do from time to time) and put himself in a compromising situation that led him to do that which he normally would not. In the final analysis, based on 2Peter 2:4 - 9, God ultimately forgave him for his errors.