So I've told my parents I'm otherkin, and I'm trying to help explain this to them. It would be helpful for some people who have been through this and are really experienced (Like you guys here!) to help simplify and explain this to them.
When I explained it to my mom I just told her otherkin were people who identify as non human either spiritually or psychologically. Someone who believes they were a dragon in a past life is otherkin. Someone who psychologically identifies as a dragon is also otherkin. We just identify as non human in some way. I told her I identify as a catgirl, then had to explain what a catgirl is. I did the same thing with my therapist.
I just tell people I feel like a dog, but know I'm human. 100% physically and neurologically human, I accept that. But I feel like I'm internally part animal and want to express that in completely harmless ways.
Seeing as this is post incident this advice has little value but I will render it all the same.
The first and most important question always is, is "Do they have a need to know?" Will telling them improve the relationship? Is it worth risking rejection and hurt? Is it something that one can go on without doing lest it weigh on their conscious?
If the answer to any of this line of questioning is "No.", the individual should reflect on what is driving that urge and what consequences would come from it; the weighing of pros and cons. I mean that sincerely too, that this is critical because what one might mean very honestly and for the sake of being noble as well as forthright does not mean mundane persons will receive this so well.
The second of these things is to frame it in a way that people are familiar to and can understand in modern parlance. The idea of therians and therianism, the psychological and spiritual halves respectively which also apply in more broad concept to otherkin as a whole, is no revelation. The ideas of being more than human or desiring to be and aspiring to be, to become "divine" in a way is prehistoric. Which is to say this is nothing they cannot understand, rather it is an exercise in presenting the experience.
The best ways in which I have come to explain it to people is that is akin to reincarnation, the idea of the transmigration of soul into a new form. That another avenue is that one has a spirit animal and that it is them, that they are one in the same, which is a very common belief in many indigenous peoples' beliefs. Another is that it is a "power animal" or divine presence, something which sparks them and is with them, part of them - fundamentally the Holy Ghost in its original, unaltered understanding in Christianity is fascinating in its way of being similar in that it is an ethereal being and thought who animates the person who welcomes it into their heart. Obviously one can see the supposed disparity is not so much as thought and that there are many explanations as well as interpretations, a few of which I mentioned here briefly, at least in the spiritual sense whereas in the psychological one the answers tend to be a bit more dire.
The therian and otherkin phenomenon all have telltale signs of identity disorders or really more specifically tropes of dysphoria and or dysmorphia. While not a recognized disorder, by which I mean the major medical condition listings for and in billing to insurance, "species dysphoria" is a subset of the greater whole and is not widely known because of its relatively rare quality - extreme infrequency - and that many of the hypothetical sufferers are functional compared to other dysphoric persons. I should also note dysphoria is a pervasive, underlying, relentless, consistent sense of unease and discomfort, in this case relating to the reality that the individual perceives themselves to be something other than human and are troubled by this subconscious nagging that some parts, alternatively all of them, are not right. Only a licensed clinical practitioner in psychology or psychiatry ad therapists should make the ultimate decision about this but it is a very real thing, something tangentially related to gender dysphoria - formerly "Gender Identity Disorder" or "GID". I strongly advise that if this is the case or if one believes it to be that they seek professional assistance and in this case, with the help of their parents. I say this because major anxiety, depressive, and mood disorders - as well as other conditions that may be inhibiting the best quality of life - are likely to manifest or worsen.
Allow me to state the psychology of "otherness" should not be treated simply or completely as malicious to the individual. Some of us, myself included, draw from twin wells - that psychological and that spiritual. It is a driving force to not only live up to what I could and should be in the world, even if I only am in the mental one, but also that I am called by divinity to be more than I am. It is an aspiration and path to take for life improvement and self-discovery. It is part of the process of actualization and individuation, the process of learning and being who one is from all their disparate parts into one sum within their mind and spirit, good and bad.
i hope that this post provides you with something, that it helps explain and open those doors needed, helps lead to those answers required, @Leaniz.
Maybe I can add something in addition, although @Red-in-Tooth mentioned a lot of things already. Let me put forward that I did not tell anyone irl about my identity thus far; still I'd like to offer an opinion because I pondered about this a lot. In general, I totally second the thought that one should consider very carefully whether or not to tell others about their otherkin nature; to be honest, I would tend to stay at the safe side unless there was a profound reason to tell. After all, we have to see that the sheer idea of feeling other-than-human may be unbelievable, outrageous or even offending for some, depending on their individual beliefs. One of the least harmful things you can be faced with is misunderstanding or non-understanding; the worst thing is making people trying to "remove" your identity from you, which can be very harmful. That's why one should also be very sure about their identity before even making the attempt of explaining, and be ready to face critical or offensive questions.
But anyhow, you mention that you already told your parents, so maybe there's no way back now (unless you'd label your own telling as a joke or similar, which might be not too credible). So this is not about carefully explaining as much as to make sure that they don't misunderstand. If you've explained the basics, I'd suggest to be very clear in stating that being otherkin is not something that can be removed or grown out from; it's something deeply intrinsic to your identity. One might be wrong or unsure about their kintype, though; if that is the case (and your kincard mentions that you only awakened this year, so it'd be natural), I think it's better to indicate that unsureness instead of claiming otherwise. Also, it might be a good idea to indicate that you're still exploring this, are critical about your own identity, and very aware of how unlikely it may seem. At the same time, I'd make clear that it's not some gameplay or something I chose just for fun, and that it's absolutely and certainly no joke. Also make clear that this is not a religion or sect, and that you're not influenced by anyone. If you'd like to mention the community, make clear that we're not here to push you into anything, but provide help and give careful advice. Whatever you say, I think it's crucial that the explanation comes across in a very calm and rational manner, but also such that it's clear that you stand your ground.
You see that this is not at all an easy task. Depending on the belief of the person you talk to, and given that there is a minimum level of willingness to understand on their side, I think one might get anywhere between (doubtful) acceptance and (to some degree) understanding; however, to fully understand what it entails to be otherkin, I think one has to be otherkin. It must be extremely hard to wrap one's mind around the possibility of feeling non-human alone, so I think it may be almost impossible to really understand what it entails unless you experience it.
I wish you all the best in explaining yourself - keep us informed and feel free to come back to us if you face problems!