Many Parrot species are not as social as we might think. In the wild they live with only one partner or small family groups. Flocking may only happen under certain circumstances such as foraging or roosting. Therefore automatically accepting new individuals may not be the norm for those species. Learning history also plays a role in how quickly a Parrot may be inclined to respond to a new potential friend. That is where training can help.
Even though your Parrot's behaviour may present challenges that might be a bit different from your dog or cat, don't give up! They are often eager students and ready to learn.