Why see a flying pigeon with a twig in its beak?

A flying pigeon with a twig in its beak is likely building a nest. Pigeons are monogamous birds that mate for life and build nests together. The twig in its beak is likely part of the material the pigeon is gathering to construct its nest. Pigeons prefer to build their nests in sheltered locations such as tree cavities, ledges, or roof eaves. The twig may also be used to line the nest for comfort and insulation. Pigeons are also known to be very loyal to their nests, and will often return to the same nest year after year.