Ah.... Looking at the Matches for Sarah Neely adds a bit of clarity ...
One MH tree identifies parents Robert Carothers & <private>. However, two others (different tree owners) identify Hugh Carruthers, Sr.(1747 - 1782) + Sarah Purviance(1710 - 1799) as parents. These are the same that have wife Sarah Neely's parents with some apparent reliability.
Not all are consistent, though: another couple of MH Tree has John's parents as James Carothers+M. Caldwell or Carothers (born Morrison).
There does seem to be some consistency that "John C. Carothers" had parents of Hugh Neely & Sarah Purviance.
There are two WikiTree matches to wife Sarah Neely-1727: one has John's parents as unknown, and the other has him as "Son of James Carothers and Esther Quigley".
... now I'm going looking for a John C. Carothers to see if that sheds any other insights ...
That Hugh & Sarah, Jeff, could just have incorrect dates ... something else to look at ... but a quick look at the ones originally connected as John's parents seem to have consistent dates with their surrounding profiles.
Note in my previous reply that Hugh1747 would be too young to be John's father (as Jeff said), but a 1710 Sarah Purviance could fit -- which got me looking at John's birth date alternatives, which range from 1725,26,27, 1730, & 1736. The 1736 doesn't work well with marriage and children's birth; 1725-27 is reasonable (and, by the way, would fit with a 1710 Sarah Purviance).
Looking for James Carruthers ....
perhaps this would also help a bit
http://www.geocities.ws/longwellgeneology/volume43.txt
http://www.rootsweb.ancestry.com/~ncschgs/carothersfam.htm
http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=42608331
http://familytreemaker.genealogy.com/users/w/i/l/Lisa-Williams-18/W...
http://www.smokykin.com/tng/getperson.php?personID=I7142&tree=s...
Having looked at them:
1) (geocities) seems to indicate a father Robert, but not much to go on.
2) (rootsweb) nothing about parents
3) (findagrave) seems to be a different John Carothers: birthdate too late & rather different death date. **However** that does seem to rule out parents of William & Joan as they would be too young for this John, particularly with a 1725-27 birth date. So, that is helpful to possibly eliminate the currently-attached 'William-1714' as father.
4) (familytreemaker) This one looks like what much of this is based on -- except that when one starts looking at timelines: If John was born in 1739 and married in 1748 -- that's at age 9 and first child at age 11. And that 1748 marriage is the 3rd marriage? It is unlikely ... and calls into question the dates of the parents of John as well ( William Carothers-1714 and Jean-1718 ). Examining the Source listed for all the parts of that family, it is a "One World Tree" database from MyFamily.com (LDS).
5) (smokykin) This one has similar relationships to #4, but doesn't assign birth dates to John nor his parents William & Jean. It does provide a birthdate for John's sister Margaret as 1702 ... which is quite a bit earlier than a 1725 birth for John, but not unreasonable if Margaret was a half-sister (as one of the others implied).
#5 has wills for both William & Jean, making this the best reference so far that John's parents are William & Jean.
http://www.smokykin.com/tng/getperson.php?personID=I7140&tree=s... - William
http://www.smokykin.com/tng/getperson.php?personID=I7141&tree=s... - Jean
My subsequent looking at link #5 actually makes the FindAGrave more possible, but that birthdate certainly doesn't work for marriage & children! The actual death date is a bit muddled, too, as some seem to confuse the Will dates (first witnessed, updated, & 'proven' dates) with death date. (John's will is posted on his About).
FindAGrave mother of Joan vs. Jean is an easy mis-reading, particularly of handwritten script.