In Terminator 2, John Connor and the company
attack the Cyberdyne Systems research department, and destroy all the things that could lead to creation of Skynet.
After that we see T-1000 coming to the place and learning what they've done. Why does he keep pursuing John, if
the system that sent him is destroyed?
It's just not logical. The T-1000 has quite an advanced intelligence. Let's imagine that a killer got an order from a client to kill someone. But before the killer executed the order, he suddenly learnt that
his client is dead, perhaps shot or the victim of a heart attack.
What is the point of killing someone after that? Just keep the money you got and don't do anything — that seems pretty reasonable.