If we can only prove that an inconsistent system is inconsistent, and we can never prove our (presumably) consistent system is consistent, then it is incomplete.
We can't say it's inconsistent just because we can't prove otherwise. We can say it may be incomplete (or inconsistent, and we haven't noticed yet)
We can't say it's inconsistent just because we can't prove otherwise. We can say it may be incomplete (or inconsistent, and we haven't noticed yet)