Not even close to true.

"My paramount object in this struggle is to save the Union, and is not either to save or to destroy slavery. If I could save the Union without freeing any slave I would do it, and if I could save it by freeing all the slaves I would do it; and if I could save it by freeing some and leaving others alone, I would also do that." - Abraham Lincoln in an open letter to Horace Greeley, 1862.

Colonization was widely supported pre-Civil War by leaders of the Black community as well.

Maybe in a world where being freed in the USA seemed impossible, and from a place of struggle. Not out of the mouth of the most powerful man in the country AFTER these people were made free.

Out of no small concern for the prospect of a guerilla war sparking up - something which the KKK several years later, thankfully after the Confederates had been largely disarmed and disbanded, did end up creating in response to losing their 'privileges' over Black folk as part of Reconstruction

Leaving Confederates largely in power is exactly what led to this. The system had to be dismantled not wishy-washy "oh just say you're loyal now and you can go back to your life". This left Confederates in a position in society that hugely hampered financial and societal freedom of the freedmen in a vicious, self worsening cycle setting them back into a spiral of poverty that led to nearly as bad conditions as slavery.

People are products of their time

There are people from that time with FAR better views and actions than Lincoln.