Penelope not only desires to offer hospitality to the stranger (as ancient Greeks permanently kept in mind that gods liked to mask), but she also wants to reestablish last bits of instruction by representatively placing the beggar, as a visitor, next to her son. The beggar is being ill-treated and hit out by the suitors, so this action means that she is still the presenter and young Telemachus the host, and their discussion is important. Moreover, the beggar is filthy, old and in rags, while the suitors are fresh, amusing, attractively dressed, and decent - but then again still no one of them is given the righteousness of sitting next to Telemachus. This would perhaps have the effect of putting the suitors down because of their rudeness.
1 Reasoning: the drawing of inferences or conclusions from known or assumed facts; the use of reason. 2 Critical thinking: To evaluate and judge the accuracy of statements and the soundness of the reasoning that leads to conclusions.
