I apologize that no one has responded to your question sooner. Different experts come online at various times. I just came online and saw your question. My name is ***** ***** I’m a biologist with a special interest in birds. I'm sorry to hear of this incident.
We can't assume the father did this because it may have been the mother. There are several reasons this may occur. A normal clutch size for umbrella cockatoos is only 2 or 3 eggs. With too many eggs, the parents know instinctively that they cannot care for so many and will destroy them. They can also sense when something is wrong inside an egg, and will destroy an egg for that reason.
Another possibility is that the mother has a nutritional deficiency. In that case, she may eat an egg or its contents in order to obtain those nutrients.
Diet is the single most important factor in keeping our birds healthy. Many people still feed a diet consisiting mostly of seeds, but recent research has shown that an all-seed diet is not good for cockatiels. Pellets, supplemented with various fresh and healthy “people foods,” along with a few seeds make up a healthier diet. Birds that are fed mostly seeds tend to develop fatty liver disease, tumors, and other health conditions. however, if your birds are used to eating mostly seeds, you’ll have to convert them to pellets gradually. The following two sites are where you can get reliable information on feeding and care. The second one has a section on converting from seeds to pellets. It applies to all birds, not just cockatiels.
Also be sure to provide both cuttlebone and mineral block.
Finally, sometimes eggs get broken accidentally. The parents will then eat the eggs to keep the nest clean. Sometimes once birds taste the contents of an egg under these circumstances, they develop a taste for them, and will break eggs deliberately. When such a habit develops, the eggs have to be removed to an incubator. I hope that won't happen.
We don't have any way to know exactly what happened, but any of the above reasons are possible. I hope it won't happen again. Just let me know if you have more concerns.
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