The normally cool and collected Karenin loses all ability to reason when he watches a woman or child cry. When Anna weeps on the way home from the races, Karenin refuses to look at her, which makes him look like death to Anna. He feels strangely liberated, like a man who has just had an aching tooth pulled out.
Karenin is touched by tears, proving he has a heart under his cold exterior, but he refuses to allow himself to empathize with Anna. The comparison of Karenin’s removal of pain to a tooth removed is one of the many very physical, embodied descriptions Tolstoy uses.
Karenin muses about female infidelity in society. He dismisses the idea of a duel with Vronsky. Karenin also dismisses separation or formal divorce, because of the societal scandal that would ensue. He decides that the best solution is to make Anna stop seeing Vronsky and for the marriage to continue; he believes that Anna and Vronsky should not be allowed to be happy, because they are guilty.
Karenin plays through all the possible options in his head, somewhat mechanically. Saving his social reputation is extremely important to him, but he also does not want Anna and Vronsky to be happy, as this seems unjust to him and in his righteousness (which Anna earlier admired) he believes the guilty must be punished.