President Johnson was quite different from Abraham Lincoln, to say the least. From Tennessee, Johnson was a southerner at heart who believed very strongly in states' rights. He didn't like the idea of a federal agency like the Freedmen's Bureau being a part of any social re-engineering of southern society. He had recommended that southern states be readmitted under Lincoln's 10% Plan, and that they had met all of his conditions, but Congress completely disagreed and didn't want the southern states let off the hook so easily, until at least they had approved the 14th Amendment giving freed slaves citizenship. So they passed the Freedmen's Bureau bill as a way to push civil rights, and Johnson vetoed it on those grounds alone.
In addition, Johnson just didn't like Congress (the feeling was very mutual). Dominated by ardent reconstructionists, Johnson felt marginalized and ignored, and liked to flex one of the only political muscles he had: the veto. In vetoing the continuation of the Freedmen's Bureau in 1866, he started a running battle with Congress which then passed a series of civil rights bills, knowing Johnson would veto them, and then passing them over the veto anyway with a 2/3 majority.