The logic behind “ren” or “renny,” is that it is short for “parent,” in the same way that Mom/Mommy and Dad/Daddy are short for mother and father, (completely ignoring the fact that Dad doesn’t make a damn bit of sense.)
The suggestion here is that parent is gender neutral, and should thus be used as the basis for a gender neutral term. The only problem is that parent is NOT, in fact, gender neutral, at least not entirely.
The fact that ren/renny’s wordsmiths chose to exclude “Pa” from their derivative, as the isolate itself is a prefix denoting that something is of or pertains to fatherliness, clearly demonstrates a gender association which even they could not ignore.
To truly be gender neutral, the new word must ignore the word parent as a gender neutral root, and instead look towards the roots of mother and father.
father comes from faeder, and mother comes from modor, but unfortunately no gender neutral equivalent is known to exist. The two words are similar, which is why their derivatives are similar as well, and while this might not hold true of a gender neutral root or it’s derivative, we can infer that they would.
SINCE there is no etymological basis for a gender neutral, and we are assuming similar morphology even if there were, we must look at the current forms of the two words, father and mother, to extrapolate the gender neutral.
The common portion of father and mother, “ther,” need not be altered as it is already gender neutral on account of it’s commonality. We must instead look only at what’s different and determine it’s mean. In the case of father and mother, what is different are the first two letters. We therefore need only find the mean prefix of of the prefixes “fa” and “mo,” and combine them with the already gender neutral ther.
To determine the mean prefix, we first need to break the prefixes into their constituent pairs of F and M, and A and O.
Obviously the mean of two vowels would need to be a vowel, so we will exclude consonants entirely from this determination. Two vowels fall between A and O, and they are E and I, there is no basis for deciding between them, but fortunately the two are often paired together, and we will therefore do just that.
The mean letters of F and M are I and J, but just as with the vowels, the mean of two consonants should be a consonant, leaving J as the mean of the two.
The gender neutral of father and mother would therefore be “Jeither.”
To construct the short form, we should only need to take the prefix and attach it to it’s first letter, giving us “Jeij.” Due to the incongruity of the word dad however, things get a bit more complicated than that.
The short of father should be “faf,” but instead we replace the F with a D resulting in dad. D comes two places before F in the alphabet, but we can’t simply follow this same model as mom doesn’t and it therefore wouldn’t be gender neutral to do so. It also wouldn’t be gender neutral to ignore it either.
Instead of going two letters back from J, we should instead go one letter back, but this doesn’t work either, since one letter before J is I, and we’ve already excluded vowels. Excluding vowels would make two letters back G, and one letter back H, but we can’t do this EITHER, because H is ACTUALLY two letters behind, and some might argue we’re using circular logic to favor the patriarchy. Instead we must find the mean of H and J, but how does one find the mean of two letters where no letter exists between them?
Just as with E and I, we’ll simply use both letters. This gives us “Hjeihj” as the short form of Jeither. But how does one pronounce Hjeihj, and more specifically the combination of H and J? Much of English is derived from German, and fortunately for us German and Swedish are very similar languages which share a common root. There are rules in Swedish for how to pronounce Hj, such as with the name Hjalmar. Put simply, HJ is pronounced as a Y. This means that Hjeihj would be pronounced as “Yeiy,” but as we all know, American’s are culturally inept and pronounce everything wrong, often intentionally. To simplify proper pronunciation, we’re going to forego the Swedish spelling in favor of the phonetic spelling.
In conclusion, the gender neutral of mother and father is jeither, and the gender neutral of mom and dad is yeiy.