What ARE birds?

For reference:

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Spoiler

• All birds are animals, but not all animals are birds.
  
• Humans are birds.
  
• Not all reptiles are birds.
  
• Not all mammals are birds.
  
• Not all invertebrates are birds.
  
• Not all birds are birds.
  
• Not all animals larger than humans are birds
  
• Not all animals smaller than humans are birds
  
• Not all pets are birds
  
• One member of the crocodilian family is a bird.
  
• Sharks are not birds!
  
• Dogs are birds.
  

• Cats are birds!
  
• Not all furred animals are birds
  
• Not all brown animals are birds
  
• One member of the crocodilian family is a bird
  
• One member of the alligator subfamily is a bird
  
• Gharials are birds!
  
• Caimans are not birds!
  

To clarify: This topic requires specific classification (i.e. taxonomy), so for reference, crocodiles, alligators, and gharials are not in the same family, but alligators and caimans are.

Hint:
Not all species are birds.