Biography
This character has a natural empathy for other life forms. They talk to animals that don't normally go near humans. Their garden is a work of art and they gossip with the flowers. They predict the weather by listening to the birds and can foresee a drought by examining the plants. Sometimes this is a very general ability encompassing all of nature, sometimes it's exclusive to one particular species. But either way, they have a special relationship with some non-human being on a level other humans can only dream of.
The problem? It's a totally different story when it comes to the members of their own species.
The price for communing with nature is apparently a graceless ineptitude with other humans. You might find them deep in conversation with a lion, unicorn, daffodil, alien, robot or many-tentacled people-eating thing, but a simple "good morning" on your part is liable to send them scurrying for cover or provoke a tirade.
Broadly speaking, there are two variations of this character.
Shy
The shy type is a sweet natured little soul who simply doesn't understand humans. They're so noisy, and they fight all the time, and they ask awkward questions and...(here the train of thought breaks down as they start hyperventilating and go fleeing back to their farm/garden/whatever). When it comes to taking care of sick animals or wilting plants, however, they can show remarkable courage and tenacity. If The Hero and his merry band need his/her help, they'll have quite a job on their hands to earn enough trust to win him/her over. Nearly invariably, they manage it.
If the character who's Not Good With People joins their group and becomes a regular cast member, they suffer some mixed fortunes—The Lancer will probably enjoy teasing them and sending them running for cover, but at least one other member will adopt a shepherd role and stand up for him or her. They can also be surprisingly successful romantically; the animal-plant empathy combined with their inherent sweetness can see them walking off with a pretty guy or girl on their arm while more assertive types snarl in envy (although much will depend on whether the writer favours good guys and nice girls, or spitfires and rebels).
Grumpy
The grumpy type is much more active, but far less benign. Unlike the shy type, who seems to symbolize the fluffy, gentle and "pure" nature of...well, nature, this type abides by the law of the jungle and is much more pragmatic. This approach can extend even to the species that they're "connected" to. Rather than singing to the flowers, they'll probably prune them in a businesslike manner and lecture them on last year's poor growth rate. They will however, give them a smile and an affectionate pat when they do well, and the plants will love them just the same.
Though they're just as talented with animals and/or plants as the first type, they're not afraid of people — they just don't like them. The traits that their brethren find "scary," they find "annoying" or "disgusting." Talk to them and they won't run away...but brace yourself for a rant on how all Humans Are Bastards and why should they bother helping you when you're just a member of the scummy species they hate the most?
Admittedly, often their bark is worse than their bite. Those who prove to them that there is something salvageable in human nature (through, say, a Patrick Stewart Speech) might manage to win them over, setting then up for better interpersonal relations...or just prepared to make an exception for one or two humans in particular. Even if they do, their non-human buddies will always be first in their affections. If they don't...well, then they're a nature-loving Jerkass whose talent with animals or plants supplies their Pet the Dog moments.
Sometimes their dislike of humans results from spending so much time with other species, putting their experiences as homo sapiens in a new and unflattering perspective. Sometimes it's the other way around — the character's hatred of humans actually drove them into developing a bond with some other living being.
If a grump becomes egotistical enough, to the point that their "gift" is more an intellectual ability than an emotionally-based talent, then they become a variant of the TV Genius.
The sci-fi genre in particular has seen the boundaries widened by throwing in robots and aliens as viable alternatives to animals and plants. The one rule for this character is that they have a powerful empathy with some other species than their own, apparently at the expense of basic social skills.
Polar opposite of Animals Hate Him.
See also No Social Skills, which is simply social cluelessness and doesn't entail any skill with non-human creatures.
