To "mix socially with prominent executives and their wives" means, to attend social events (i.e. either work related or non-work related events housed by clients or potential clients or authoritative agencies, such as the government or the city (i.e. 'responsible civic affairs) with administrative members of the company. In Japan, making a good impression is very important, if not the most important thing in one's business and private life. As you know, that is, if you are Japanese, you may know that married men tend to be looked upon as responsible employees, inside the company as well as outside the company, because what they do in their free time, reflects on them and their family, so they tend to be or rather people assume they should be more responsible in how they behave. Single men, however, are looked upon as not caring about their reputation. What they do inside or outside of work reflects on them alone. Moreover, if they are single, there is more of a possibilty that they will strike up relationships with other single members in work, and/or outside of work-members that may have connections or say as to how the company is managed, will gain contracts, etc.Originally Posted by japanjapan
According to the paragraph you posted, it seems that in Japan, especially at that particular company, single men are viewed as a threat; married men are not.
All the best,