Huh? You talk confusingly, and do not seem to excel at making clear points.
The encyclical you quoted, first of all, should be read in historical context. If you would have done that, you may have realized it was written in response to specific things that were happening at that time. Language and the meaning of that language does not always mean the same thing today, as it did back then. So, you cannot simply pull a few sentences from it and then twist it to your own discretion.
The encyclical basically says that we do not have the "right" to be wrong. Like you said, errors have no rights. So, getting back to what father actually said, rights are "given by the creator", obviously, the creator cannot be wrong--cannot error.
So.... yeah, I don't get what you're trying to say. Maybe you should quite while I'm ahead.
An analytical statement is one where the predicate is contained in the subject.
When you said:
The encyclical reads "personal rights" (ie- created by man).
The i.e. would imply that you are saying that 'personal rights are created by man' is an analytical statement. The the predicate of 'created by man' is contained logically in the subject of 'personal rights.' Take the statement 'All bachelors are unmarried.' The predicate of 'unmarried' is contained logically in the subject of 'bachelors' since to be a bachelor is to be unmarried.
I am saying that this does not seem to be the case since the subject of 'personal right' does not logically contain in it the predicate of that right being man made. I don't believe that personal rights come from God. But, logically speaking, there is no inherent reason that they couldn't.