There is one main conflict, and a variety of other, smaller conflicts that contribute to the main one.
The obvious conflict is the external conflict that results when the Michael Obi's wife plants a garden over the path that connects the village shrine to the place of burial. The priest visits Michael Obi and explains the uses of the foothpath, and Michael Obi refuses to change his mind about allowing the villagers to use it. This is an example of a person versus person conflict.
There is also a person vs. society conflict. The "old way"--personified by the foot path and the priest--clash with the "new way"--Michael Obi's headstrong belief about not having the footpath go through the school grounds. THis could also be a person vs. supernatural conflict, because the supernatural "gets back" at Michael Obi by destroying the school right before the government inspection happens.
All of these are examples of external conflicts.
The main conflict involves Obi's refusal to open the ancestral pathway which connects to the universal conflict between modernity and traditional cultures.
The main conflict surrounds a village footpath that travels through the school compound connecting the villagers' shrine to their burial grounds. Obi, a progressive headmaster, decides to block the path because he doesn't want the villagers wandering on school grounds during an inspection. After he closes the path, the village priest, Ani, visits Obi and informs him that the walking path is an integral part of their life. Ani says that ancestral spirits and future children travel back and forth between the path. Obi, who does not believe in such spirits, does not take the man seriously and refuses to open the path. The next day a woman dies during childbirth, and the villagers seek retribution by tearing down one of the school's buildings. Unfortunately, the inspector writes a scathing review and blames Obi for inciting conflict between the villagers and the school.
“Dead Men’s Path” enacts in miniature one of the central themes of Achebe’s novels—the clash between modern European ideas and traditional African values, progressive international standards and deeply rooted local custom. The story’s protagonist, Michael Obi, is a well-educated forward-thinking idealist with a passion for “modern methods.” Quite intelligent and undoubtedly dedicated to education, Obi is more comfortable in abstract thought than in facing the complexities of real life. He doesn’t notice unspoken feelings; for example, his wife’s considerable disappointment upon learning that the other teachers are all unmarried. His view of the world is rational and therefore incapable of fully understanding the parts of life ruled by emotion, intuition, or custom. Obi looks down on the older headmasters of the Mission schools. Note how Achebe subtly undercuts Obi in the opening paragraphs. Only twenty-six, the newly appointed headmaster appears much older with his “stoop-shouldered” posture and “frail” build.
Michael Obi’s name demonstrates his divided heritage. Michael is a Christian baptismal name of European heritage. (Remember Obi works for “Mission” schools—as did Achebe’s father, who was a devout Christian.) Obi, by contrast, is an African name. His name itself embodies the cultural conflict he is about to enter.