The zero-sum mentality which leads people to think that way is already clear in The Mote In God's Eye. I think the point of the book is that despite being superior to humans in every way imaginable, the Moties are condemned to repeated violent conflict by Malthusian pressures, because they have nowhere to expand. One way I interpret the "mote" in God's eye is the authors' belief that no matter how good we get, we'll always be in potentially violent conflict with each other for limited resources. (The "beam" in our own eye is then that we're still fighting each other over less pressing concerns. :-)

Ringworld is a great book. The later books have great concepts, but could do without so much. . . rishing. Niven plainly inserted his furry porn fetish into those books, for reasons unclear to any human alive.

>I think this is my favourite book but I think his best book is maybe Ringworld.

Ringworld is pretty good, the multiples sequels get kind of out there.