Human nature is rarely a straightforward What-you-see-is-what-you-get proposition. Everyone has his or her inconsistencies. Given the opportunity, even minor inconsistencies can result in major conflicts affecting lives disproportional to their original causes.
Searching for the motivation of a character's inconsistency and exposing it to a hostile environment can produce a character with conflicts that capture the reader's active interest. In fiction conflict is axiomatic, without it you have "cardboard cutouts" rather than three dimensional personalities.
In choosing an inconsistency for a viewpoint character, first decide how long your story will be. Is it a short-short under 1,000 words, a short from 2,000 to 7,500 words, a mid-length up to 20,000 words, or a full-scale novel. The longer the work the more complicated the inconsistency can be.
For example imagine a man called Mr. Payne, who encourages his daughters as he does his sons to enter a university and work toward a profession in law, medicine, or whatever they want. He will support any goal they aim for. However, he insists that his wife's place is taking care of the home and their children. While the children were growing up, she agreed that motherhood is a full-time job. But now that the nest is empty, she is bored, she wants a job, not for the money, but for the contact with people who can discuss topics other than home, children, and the P.T.A.
Mr. Payne objects. He feels that as his wife she still has him to care for, as well as taking care of the house. She gradually begins to notice things that were previously unimportant, or just minor annoyances. Mr. Payne drops his clothes wherever he happens to be when he undresses, never putting anything away. She shops for him as she did for her children when they were young, and comes to realize that for thirty years she has been as much his mother as his wife.
All this can be shown in the first scene in about 500 to 800 words. Now that you have your conflict, you have to decide where to go from there. It's unlikely Mr. Payne is aware that he plays the role of a little boy, he simply believes that mothers belong at home. Where you go from here depends on what you want. Are you aiming for a psychological drama, a modern life tragedy, or a satire?
A possibility for a short story inconsistency motivating a character can stem from a secondary character. The viewpoint character is in the soup because she trusted another person who came across as organized, dependable, and a ball of fire. The secondary character made promises that have not been full-filled, in fact, no attempt was made to do so.
Your viewpoint character, Ms. Tower, works five days a week, eight hours a day at a job she hates. Each evening she puts in an hour or two writing. Every weekend she squeezes out writing time after the household duties. After several months Ms. Tower finished her first novel. She knows she hasn't the thick skin necessary to deal with the rejections even the best manuscripts usually get before they are finally accepted for publication -- and may never be. She also is aware that many publishers accept only agent submitted manuscripts.
Though she has a two year contract with an agent who expressed great enthusiasm for her book, he isn't delivering on the promises. In fact, Ms. Tower discovers that publishing houses the agent claimed to have contacted, and for which he charged postage and copying fees, never received her manuscript. All her works are effectively frozen until the two years are up.
This is where the story opens. You have the conflict. Your story might be a comic-suspense in which Ms. Tower uses 007 tactics to prove misappropriation of funds and other charges. Or, she could confront the other character in the first scene. In a fit of temper she accidentally kills the agent. With this scenario you have the full range of mysteries to choose from, from psychological drama to a Columbo-type fencing with the police.
In our culture religion, politics, and sexual stereotyping, are inner conflict mother-lodes waiting to be mined by the industrious novelist. A character's overt religiousness can become such a predominate part of their public-self that few, if any, see conflicting traits. This would be especially true with an inconsistency the character is at great pains to hide.
Mrs. Smith is an active church member, working on several committees. She keeps her house and children spotlessly clean, and is supportive of her husband's professional ambitions. She seems an active, happy, good person, a credit to her religious and family groups. But is she?
Mrs. Smith is a dull fictional character if what-you-see is truly what-you-get. What if Mrs. Smith secretly dislikes children, hers and everyone else's? She is aghast when she accidentally becomes pregnant with a third child. She decides to go to another county, and apply to an abortion clinic.
Sometime later, her minister and fellow church members decide to picket the local clinic. Mrs. Smith, believing that no one at the local clinic would know about her abortion, agrees to take part. However, a nurse recently transferred from the clinic Mrs. Smith attended. The two women immediately recognize each other. Mrs. Smith knows that abortion clinic workers are sworn to never name any patient under any circumstances. Yet Mrs. Smith knows her own morality - under pressure - proved situational. Can Mrs. Smith trust that the nurse, clearly growing impatient with the protesters, won't let her anger supersede her conscience?
You now have a basis for a variety plot turns, whether or not the nurse uses her knowledge to pressure Mrs. Smith. Also, Mrs. Smith's conscious is sure to throw off any restraints that she'd previously enforced. This could lead to a domestic drama when the husband learns of the abortion, a murder mystery in which Mrs. Smith is superficially unlikely to be the killer, or a psychological drama with Mrs. Smith gradually suffering a personality-disintegration. Whichever plot-line the writer takes, Mrs. Smith's inconsistency should remain hidden from the reader, with slight-of-hand foreshadowing, until the final denouement.
The next character is, Mr. Bigman, a middle-aged senior executive with a major corporation who seems warm, gregarious, and generous. He is devoted to family, friends, and professional associates, and exudes charm and charisma. Mr. Bigman has a genuine desire to improve the world in which he lives, and has the power to do so. Hardly your typical hard-nosed executive.
Well, in truth, he isn't. Mr. Bigman is two people. He is caring, but is also a cynic, a man who believes the axioms "the end justifies the means", "fight fire with fire", and "you can't make an omelet without breaking eggs". You have a good man trying to do good things, with bad methods.
He makes enemies of people who would otherwise be his staunchest supporters. Both sides want the same thing, but disagree on methods. Until the underlying conflict is resolved, the main conflict can't be dealt with, and gains speed toward a point-of-no-return. The writer must satisfactorily resolve the struggle between the two factions in the eleventh hour, so they can join forces to deal with the now critical main situation.
Your final example is Ms. Jones, a woman filled with smoldering resentment at being treated as a second-class-citizen, but is also angry at herself for having been born female. Ms. Jones knows she is worth more than the system allows. However, because of her early socialization by traditionally minded parents, she subconsciously believes that most women fit the cultural stereotype. Yet, she is too intelligent to accept this imprinting for herself.
Ms. Jones worked hard for good grades and scholarships. She graduated, with honors, at the top of her class from a major university. With great expectations she entered a predominately male work environment, and found herself confronted by hostile males who view her as an invader in their God given, exclusively male terrain.
To survive active harassment, she developed an abrasive aggressiveness contrary to her natural temperament. No intimate relationship develops because she sees men as enemies, and her deep-seated anger erupts at the slightest provocation. But, beneath the aggressive indignation is a romantic soul, desperately wanting to love and be loved. She develops ulcers and migraine headaches. Her survival-instinct being intact, and knowing she is successful in her field, Ms. Jones quits to find a less antagonistic environment.
But, a dozen years of defensive and offensive in-fighting habits are not doff in an instant. Ms. Jones continues to have relationship problems, especially with dominate males. She can't drop her aggressive armor, even though that protection is no longer necessary. Ms. Jones can easily become a killer or murder victim, or the viewpoint character in a psychological drama who works through her internal conflicts. In understanding Ms. Jones, the reader loses the antagonism she inspires, and feeling sorry for her, roots for her to win.
All these examples have both external and internal conflict. By imbuing the characters with multi-faceted contradictory personality traits, you develop believable three-dimensional characters.