If you want other birds to frequent your yard you need to attract them, either by the food you offer or the birdhouses you have, each type of bird likes certain houses and certain food, catbirds don't usually come to seed feeders, so you won't have more attracted by them
RESORT2ME Unfortunately, we honestly cant pick and chew what type of birds frequent our gardens any more that I can select the squirrel's that chomp away my bird feeder or the deer that demolish my shrubs, prized Roses ect.
All we can do is make is difficult for them to visit, IF bird feed is what is attracting the birds you dislike, it is a case of trying to make it harden for them to reach the feed, I hang up-turned Wire Flower baskets on top of feeders, this means the larger birds like crows cant get onto feeder but little birds still can.
IF they are feeding on insects, then they will honestly NOT be harming the birds who visit for the seeds and bird feed you are supplying for them.
Nature has it's own way of fixing out any predatory positions or pecking orders that happen the world over between different types of birds, animals etc, I know when the Squirrels come sit inside the containers I hang up filled with bird cakes I make from melted fat and bird seeds / fruits ect, the woodpecker will only cling onto the wooden post for so long before it decides to jump onto the feeder and the Squirrel takes off like a bat out of hell, so would I with a long sharp beak about to poke me in the head / eye.
I have no idea what-so-ever what family of bird the catbird belongs to, but Hawks, Buzzards, Song Thrushes, Blackbirds, Crows, Finches, Robins, Wrens to name just a few all visit my garden, the Hawks, Buzzards don't trouble the little birds as they usually search for moles, voles etc, the Sparrow Hawks however are self explanatory, and will swoop down and try grab one of the little birds who all scarper off when they see one of those large birds, I place the feeders very close to shrubs /trees ect that offer shelter/ protection for the other birds and the Hawk takes off for more fruitful places to hunt, Yes there will always be the odd time where the Hawks can take one of the little birds but hey, I eat lamb, beef, pork, Chicken ect, so let's be real about ALL creatures feeding.
As stated before, seed / fruit feeders wont bother the birds that want to eat insects UNLESS times are really hard in winter where it becomes the desperation times and survival of the fittest.
In communities where there are humans, it very rarely reaches desperation stage by fact that we humans are not good at clearing / hiding all waste and birds will seek crumbs, insects, seeds, berry's, for survival no matter where in the world,
I would suggest you look further into why the other birds are not visiting your garden, is there a cat / dog, or other animal very close by, like your neighbours pets ect, also look see IF you have created the right environment for ALL the birds, garden birds dont like too open spaces without branches, foliage etc to take refuge IF predators are around, this also allows the birds to take turns feeding in a safe area.
Also have you sited your feeders where the bird hear you or other humans too close, it's a case of reading, learning and adjusting to the wildlife's needs rather than expecting them to adapt to our ways. I absolutely love all the wildlife that visit my area but believe me, I'm still learning about there needs and habitat, even those pest deer are a joy at times.
Hope you can find ways to sort out the problem your having but honestly, I will be more than surprised IF it has anything to do with one single type of bird.
Good luck. WeeNel.
Robert, we managed to chase away most of the squirrels and crows invading the garden with one of the large water blaster water guns...it shoots a pressurized stream of water 30+ feet. I also use a slingshot with acorns for ammo. The water and acorns do not do any damage, but they certainly startle the heck out of the critters and after a while, they seek a more amenable place to hang out.
Birds startle easily...and they prefer places that are "undisturbed"...that being said, I think I have never seen a bird as persistent as crows or buzzards...and neither of them like the Water Blaster...grin I consider it a humane way of serving an eviction notice...so, with a bit of diligence I think even the cat birds will catch on...
Do continue to provide spaces for the cardinals...we gave up on traditional feeders here. Now we just put sunflower seeds in a clear open place in the driveway and every morning and evening we have a polyglot of diners...Chikadees wrens finches...Cardinals doves and bluejays all manage to eat together...crow free.