First off, I believe the premise of your question is wrong. Nowhere in the text of Chinua Achebe's short story "Marriage is a Private Affair" does it say that Nnaemeka's life was a tragedy. In fact, Achebe comments at one point in the story that word had gotten back to the village where Nnaemeka's father lives that the son and his wife were very happy.
The tragedy is in the cultural and generational gap in the story that keeps Nnaemeka's father from seeing his son for eight years. The father basically disowns him over the son's marriage to a girl from a different ethnic group. Nnaemeka is Ibo and his wife, Nene, is Ibibio. Because they live in the large city of Lagos the marriage is accepted. In Nnaemeka's small village, however, the marriage is widely condemned by the villagers. In fact, the marriage is a major topic of conversation among the men of the Ibo village, making the title of the story quite ironic.
In the end, the reader is even led to believe that the hard hearted father may one day see his son again after receiving a letter from the wife which reveals the couple have two sons who would very much like to see their grandfather. So, in fact, the story may not be a tragedy at all. Instead, it may be a hopeful precursor to a more enlightened attitude among the Nigerian people.