IN A NUTSHELL , APE LINCOLN REJECTED THE CLAIM THAT HE WAS AN ABOLITIONIST.
THERE IS NO EVIDENCE THAT HE SUPPORTED THE 13th AMENDMENT PRIOR TO THE COMMENCEMENT OF THE WAR.
Abraham Lincoln was not an abolitionist- yet he ended up abolishing slavery- odd eh?
He didn't support the 13th Amendment prior to the war- because the 13th Amendment didn't exist then.
But if you mean- he didn't support the ideal of the 13th Amendment before the war- almost certainly true- the experiences of the war led him to support the 13th Amendment and help push through the legislation
Lincoln at the beginning of the war was in favor of compensated emancipation- the Confederacy rejected that and lost all of their human property.
Some people still object to the actions of Lincoln that resulted in the end of slavery in the United States.