Jealous Birds 

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Let's say you have two or more birds and they get jealous of one another and don't let you hold the other. What do you do?
My daughter has a Crimson conure, vibrant colors, but she DOES NOT like for my daughter to hold other birds!
Birds have social structures and there is always someone at the top of the 'Pecking Order.' This bird gets priority access to food, to a better perch and they get to say whether you can be with another parrot or not.
In this video I am holding Kailani, my Catalina Macaw- even though she is ten years younger than Lorenza, my Yellow Naped Amazon, Lorenza doesn't get defensive in any way. On the other hand, Lorenza pulls rank next to smaller birds - size does matter with birds and heavily influences the pecking order. Emerald, our Hahn's Macaw, is smaller and was given to us a couple of months ago, so Lorenza generally does not tolerate Emerald being on the same chair that Lorenza and I are on. In the video Lorenza and I head to Emerald's open cage, but she quickly goes and hides in her cozy.
If you are at the top of the pecking order then you should be able to hold any bird you like without other birds making too much of a fuss, if at all. On the other hand, if one of your birds 'doesn't allow' you to hold another, this bird thinks that he/she is the top dog! If that is the case, try working on training your bird. This can help establish you as the 'leader.'