The most relevant response that helps explain why Abraham Lincoln won the election of 1860 is: Democrats were divided.
During the 1860 election, the Democratic Party was split into Northern and Southern factions, which weakened their overall electoral appeal. This division allowed Lincoln, running as the Republican candidate, to secure enough votes to win the presidency despite not having widespread support in the Southern states.
While other factors such as the unpopularity of slavery in some areas and Lincoln's stance on the issue contributed to his victory, the division within the Democratic Party was a critical reason for his success in that election.