What are sociological reasons why men in full-time work are paid more on average than female full-time workers?

Much of this, as stated in Paepin's excellent answer, has to do with historical factors. In patriarchal societies, there was a gender based division of labor, with traditionally male tasks being monetized and the value of female activities in the domestic sphere (child rearing, making and maintaining clothing, housework) not being assigned monetary value. This connection between traditionally female care-giving or domestic labor and a lack of monetary value has led to an ideology that care-giving is a task not associated with money. Thus while one expects people in traditionally male professions such as bankers, engineers, architects, or managers to demand high salaries for their skills, female teachers, nurses, or social workers are often condemned as "greedy" when negotiating for higher pay and are expected to do highly demanding and skilled labor out of an ethos of "caring" rather than demanding equivalent compensation for equivalent work. Even when women are in traditionally male professions, they are often condemned as "greedy" or "ambitious" when they ask for salaries or positions equivalent to those of their male counterparts. An excellent example of this is that Hillary Clinton was pilloried by the press for accepting speaking fees less than those charged by Donald Trump, Rudy Guilani, Tony Blair, or other prominent male speakers who are not normally condemned for high speaking fees. 

Gender segregation accounts for a significant part of the wage gap, with predominantly male semi-skilled labor fields such as construction, plumbing, or manufacturing paying substantially more than equivalent "feminized" jobs such as secretarial work, house cleaning, child care, or food service.