To be sure, a few special types of behavior come to mind. Praying, exploring outer space, and being a lawyer are, as far as I know, three uniquely human activities. But we do not do many things that another species does not also do. Even gift giving is not a characteristic unique to humans.
Many animals are gift givers.
Our dog Gilbey is not noted for aggressive behavior. His role as a watchdog is to bark so that Nero, the real dog, knows that danger lurks. I'm not sure what Gilbey would do if actually put to the test. They put the baby on a blanket in the floor to do whatever babies to while grown-ups are talking. When the dogs came into the room, each gave a disinterested sniff at the baby and then went about doing whatever dogs do while people are talking.