By the end of the film the T-800 wasn't just a mindless cyborg following a mission, it was it's own entity. He was just as much involved and interested in the destruction of Cyberdyne as John and Sarah was. In fact, it was mostly his idea to "prevent the war".
I just saw the ending as the Terminator's full understanding of the situation. The T-1000 is destroyed, he himself is on his last leg. If he exists, he is essentially the future (like that cut line alludes to). He understands he has no real purpose now and must sacrifice himself to prevent the war. He can override John's orders because he can think and choose to. While he doesn't feel and can't cry, he can think like a human being.