Ethan does not like Denis Eady as he is jealous of him. Unlike Ethan, who is shy, unhappily married, and struggles to make a living, Eady is a confident, successful young businessman, like his father before him, and particularly popular with the girls.
Ethan is particularly riled when he sees Denis dancing with his wife's cousin, Mattie Silver, whom he has feelings for. Ethan silently fumes as he watches the two together:
Hitherto Ethan Frome had been content to think (Denis Eady) a mean fellow; now he positively invited a horse-whipping. It was strange that the girl did not seem aware of it: that she could lift her rapt face to her dancer's, and drop her hands in his, withou appearing to feel the offence of his look and touch. (chapter 1)
As can be seen from this quote, Ethan's jealousy colours the whole scene. In his eyes, Denis Eady is full of impudence and nothing short of a cad; he wonders that Mattie can even bear to be near him.
After this dance, however, Mattie declines to walk home with Eady, which greatly encourages Ethan. It turns out that she has feelings for Ethan too; but their love story is fated to have a tragic end.