you tend to have some knowledge of hawks, but red tails CAN go after birds, DO go after birds, and DO go after prey that weigh more than them. they are our most adaptable buteo hawk and are opportunists who hunt a variety of prey.
for example, red tails can and DO fly off with eastern cottontails. theyre a rabbit that weighs quite a bit...
for example, from wikipedia:
This rabbit is medium-sized, measuring 36–48 cm (14–19 in) in total length, including a small tail that averages 5.3 cm (2.1 in).[12][13] Weight can range from 800 to 2,000 g (1.8 to 4.4 lb), with an average of around 1,200 g (2.6 lb). The female tends to be heavier, although the sexes broadly overlap in size.[14][15] There may be some slightly variation in the body size of Eastern cottontails, with weights seeming to increase from south to north, in accordance with Bergmann's rule. Adult specimens from the Florida Museum of Natural History, collected in Florida, have a mean weight of 1,018 g (2.244 lb).[16] Meanwhile, 346 adult cottontails from Michigan were found to have averaged 1,445 g (3.186 lb) in mass
Eastern cottontail - Wikipedia, the free encyclopedia
but if you look:
http://m5.i.pbase.com/g6/35/779835/2/150028995.40xO0Tuq.jpg
http://www.miriameaglemon.com/photo_gallery/Birds/Bird Images/P5290798 Red-tailed Hawks Sta Marg.jpg
http://i1.ytimg.com/vi/M5X8ZrHYKss/maxresdefault.jpg
yes theyre main prey MAY be mammals, BUT they do and are capable of taking birds.... for example, you can see wild birds below that wound up as prey items.
https://uwaterloo.ca/ecology-lab/si...es/resize/uploads/images/P2050040-300x225.JPG
http://www.shaughey.com/images/Hawk/Hawk.jpg
this one is a broad winged hawk, a buteo, a cousin of the red tail, another who specializes in reptiles, amphibians, and rodents, but still quite capable of taking birds
http://ninnescahlife.wichita.edu/sites/default/files/private/images/9_22_3R_copy.jpg
i'm sorry, but it is a great injustice to the red tail to claim that it is not a threat and not capable of taking larger prey. and red tails arent the ONLY bird of prey out there and others are much more capable of doing damage to our PETS, who have not been raised in the wild, who do not have the needed instincts their wild cousins do to AVOID these predators. they are easy prey and hawks know this. if hungry enough, or feeding a family you can bet your last dollar that they will definitely think about taking a pet bird.
peregrine falcons. theyre a city raptor in many many many areas, in my city we have a pair who nest here and theyve made big news... they take ducks who weigh more than they do. easily. ducks are actually one of their favourite prey items. so there's peregrines who'd likely take a larger parrot. and peregrines dont kill first hit--they swoop, smash/stun, THEN go down for the kill.
accipiters are true bird hawks and theyre clever and ruthless hunters who have even been known to chase their prey on foot, drown their prey, or purposely chase their prey into windows. that could happen with a parrot as well.
its not worth the risk to assume hawks cannot do damage. even if they dont kill in the first place, is it still worth the injury to your family member?
attached are some of MY OWN photos...
sharp shinned hawk, an accipiter. long skinny legs, thin sharp talons... this bird will hunt birds as big as it is such as blue jays. this is a true bird hawk. for those who have birds up to the size of large cockatiels, this bird lives in cities and WILL not hesitate to take easy bird prey... its one who often drives its prey into windows.
talons who could do massive damage to your bird whether it survives the initial attack or not. not worth the risk or ignorance in my opinion

these are of a great horned owl, another opportunist who will even eat skunks and snowy owls!
and meet the merlin, a small falcon who will take birds larger than it. its a bold bird and look at that falcon "tooth" on its beak, which all falcons have... that notch is designed to break the vertabrae in its prey's neck... it's small, but a lethal predator, and yes that is myself holding her, a wild banded bird that i got to release, a few years back.
whether a hawk can or cannot kill your bird, its still not worth the injury and still a risk. theyre amazing birds, but people should be aware that they are clever, will take an easy meal, and our parrots have not lived in the wild and lack the survival instincts needed. most of our birds are not used to flying miles each day for food, theyre not as physically fit as their wild cousins, and they may not fully be able to defend against a hawk attack like their wild cousins could.
