In Pushkin's time, the early 19th century, duels were very strictly regulated. A second's primary duty was to prevent the duel from actually happening, and only when both combatants were unwilling to stand down were they to make sure that the duel proceeded according to formalised rules. A challenger's second should therefore always ask the challenged party if he wants to apologise for his actions that have led to the challenge.
In Eugene Onegin, Lensky's second, Zaretsky, does not ask Onegin even once if he would like to apologise, and because Onegin is not allowed to apologise on his own initiative, the duel takes place, with fatal consequences. Zaretsky is described as "classical and pedantic in duels" (chapter 6, stanza XXVI), and this seems very out of character for a nobleman. Zaretsky's first chance to end the duel is when he delivers Lensky's written challenge to Onegin (chapter 6, stanza IX). Instead of asking Onegin if he would like to apologise, he apologises for having much to do at home and leaves as soon as Onegin (obligatorily) accepts the challenge.
On the day of the duel, Zaretsky gets several more chances to prevent the duel from happening. Because dueling was forbidden in the Russian Empire, duels were always held at dawn. Zaretsky urges Lensky to get ready shortly after 6 o'clock in the morning (chapter 6, stanza XXIII), while the sun only rises at 20 past 8, because he expects Onegin to be on time. However, Onegin oversleeps (chapter 6, stanza XXIV), and arrives on the scene more than an hour late. According to the dueling codex, if a duelist arrives more than 15 minutes late, he automatically forfeits the duel. Lensky and Zaretsky have been waiting all that time (chapter 6, stanza XXVI), even though it was Zaretsky's duty to proclaim Lensky as winner and take him home.
When Onegin finally arrives, Zaretsky is supposed to ask him a final time if he would like to apologise. Instead, Zaretsky is surprised by the apparent absence of Onegin's second. Onegin, against all rules, appoints his servant Guillot as his second which was the last action to take from a noble man (chapter 6, stanza XXVII), a blatant insult for the nobleman Zaretsky. Zaretsky angrily accepts Guillot as Onegin's second. By his actions, Zaretsky does not act as a nobleman should, in the end Onegin wins the duel.