The argument of good requiring evil / bad and happiness requiring sadness also falls flat on the face if you bring it up in conjunction with a (supposedly) omnipotent creator.
If there happens to be such a thing as an omnipotent creator, which God is according to his followers, then good and happiness have no requirements. With an omnipotent creator the only reason for the existence of something is that the creator wants it to exist. There are no necessities in such a case.
If God had wanted, he could have created a world without evil and without suffering where people still appreciate good and happiness in the same way as they appreciate both now. The only reason for suffering to exist in this world is because God likes people to suffer.
The claim that good requires evil also creates some rather severe problems regarding some of the core elements of the Christian myth.
What about heaven? How will people appreciate it to be in heaven if there is no evil and no sadness in heaven?