First and foremost, the narrator of "The Waltz" doesn't want to dance with anyone, not just the man she ends up dancing with. The main reason seems to be that she's in a fit of depression. She explicitly states that she just wants to be left alone in her quiet corner of the table, brooding over her sorrows. Whatever's bothering the lady, it's preventing her from having a good time. So she really doesn't want to dance, with the man who comes over to ask her for the pleasure of the next waltz, or anyone else.
And yet, out of politeness, the narrator reluctantly agrees to take to the dance floor. But she soon regrets it. Not only does she hate the constant rushing about, which she regards as the curse of American life, she doesn't much care for the fact that her dancing partner keeps kicking her in the shins as they glide across the floor.
One senses that the young lady is a very independent-minded woman and doesn't much care for being rhythmically manhandled in this way. At the same time, she evidently feels a certain pressure to conform to the niceties of social convention and so repeatedly reassures her dance partner that it's her fault he keeps kicking her in the shins.