The main similarity between the two is a parent's avowed support for particular candidates as marriage prospects for his/her progeny. This just means that a parent has seen fit to choose a spouse for a son/daughter, without having taken into consideration the feelings or expectations of that son/daughter.
In Chapter 19 of Pride and Prejudice, Elizabeth Bennet's mother is set on marrying her daughters off. For Elizabeth, she has set her eyes on the hapless Mr. Collins. Despite her calculations, Mrs. Bennet has not taken into consideration Lizzy's temperament nor Mr Collins'. When Mr. Collins asks for a 'private audience' to pursue his offer of marriage to Elizabeth, Mrs. Bennet is all courtesy and excitement; she tells him that she is sure 'Lizzy will be very happy—I am sure she can have no objection.' Here, she is alluding to Lizzy having no objection to meeting Mr. Collins nor to accepting his offer of matrimony.
In Marriage Is A Private Affair, Nnaemeka's father, Okeke, has also chosen his bride for him. In the story, Okeke wants Nnaemeka to marry Ugoye Nweke, the eldest daughter of a neighbor. When Nnaemeka humbly protests that he cannot marry Ugoye because he is engaged to be married to Nene Atang, the woman he loves, the father is grieved beyond measure. He becomes estranged from his son and refuses to meet his daughter-in-law, Nene.
In both stories, the parents believe that their choices take into consideration the future happiness and contentment of their children. However, these parents have chosen to ignore larger considerations such as the attraction factor or compatibility issues. In Marriage Is A Private Affair, Okeke says that the only qualifications a woman needs to be a good wife is 'a good character and a Christian background.' He objects to what he sees as a useless need to muddy the waters with such unnecessary concerns as attraction or love. In Chapter 19 of Pride and Prejudice, Mrs. Bennet believes that material considerations and future financial security are excellent reasons for the match between Elizabeth and Mr. Collins. After all, Mr. Collins will inherit the Bennet estate, since Mr. Bennet has no sons. In Mrs. Bennet's estimation, a marriage alliance keeps the property in the family and assures the financial security of both Elizabeth and her parents. Like Okeke, she deems the attraction and compatibility factors superficial considerations.
Both Okeke and Mrs. Bennet also believe that their grown children owe them the respect that comes with compliance and humble obedience to their wishes.