Correctable Errors

[chuck chopper]

I have never quite grasped the "uncorrectable" errors RE: Infield Fly Rule. I have been told that:
1) If we call it, and it was in fact was not an I.F. situation..too bad. Players should had known we blew it while it was happening. ie we call Infield fly and no one catches the ball. The batter stops running, and leaves the field. Coach says "Hey-she's not out". Too bad we can't fix it.
2) We forget to call I.F., & then the ball is not caught. Coach says "Hey blue-she's out right ?", we say OH yeah I forgot. We can't fix that one either ?
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So why is it that the Ump clearly misapplied the rule in both cases, and yet they are not protestable, or correctable.