How can the ruling on the detestability of playing with pigeons be based on the actions of the people of Lot and Pharaoh, knowing that the people of Lot also had dogs and livestock? So, is it likewise forbidden to keep them?

Playing with pigeons is disliked because there is no benefit in it, and it may lead to forbidden acts, such as peeking at people's private parts or damaging their crops, in which case playing with them becomes forbidden. The dislike was not based merely on the acts of the people of Lot; rather, it was narrated from the predecessors that they were the first to do so. There is a difference between keeping dogs for guarding and livestock for milk and breeding, and idly playing with pigeons.