Yep, it's like one huge loop, some may call it a goof (but it's inevitable when writing a story involving time travel).
Because a Terminator came back from the future in part 1, and Cyberdine collected the chip and arm from it, they were able to create the Terminators fairly rapidly.... So, in part 2 they destroyed Cyberdine, but this would NEVER actually stop this event (the war) from happening.
If the original terminator had never come, it would still have been developed, otherwise it wouldn't exist to come back in the first place.
I find it really hard to explain, it's just a concept that you either get to grips with, or just say it doesn't work. Either way is fine, because time travel, at our intelligence level, is still too hard to comprehend.
Roxy has explained this answer well enough already, but I couldn't resist writing something....