Sorry you have it backwards. Taken (in these instances) is to remove from a particular place.
1. The ones in the ark were not taken there. They built it and then moved in.
2. Lot and his daughters were not taken out of the city. The left on their own. No one carried them away.
In both these cases the ones who lived were not taken but instead moved forward under their own power.
Noah listened to God, Lot listened to the angels.
The angels took Lot out of the city leading him by the hand, they were taken, not left.
Noah went into the ark but God closed the door and sent the rain that took those in the ark away from those that were left.
The ones that were left were not removed, they stayed where they were, in the area of judgment and died.
Lot’s sons-in-law (to be?) thought he was joking.
But the people who stayed behind still died. In the flood millions. and only few, that is eight, were saved, and that not in the water, but out of it.