Assuming that the answers you have to choose from are:
A. Eager
B. Prepared
C. Unable
D. Reluctant
Reluctant (D) is nearest in meaning to the word "loth."
You are loth (or loath) to do something when you are unwilling to do it, for example if it goes against your principles.
In this case, the pigeons are behaving like they do not want to "leave their houses" in spite of the danger, probably because of the panic and the attachment they have to these places. An indication of their reluctance to fly away is that they stayed in the area ("hovered about the windows and balconies") and let themselves be surpised by the fire ("till they were ... burned").