Why did the Republican Congress disagree with President Andrew Johnson's reconstruction plan?

Answer 1

A major area of disagreement between Abraham Lincoln and the Radical Republicans was that Lincoln wanted to forgive and reintegrate the South back into the Union as painlessly and smoothly as possible while restricting the rights of freed slaves, whereas the Radical Republicans wanted to punish the South as harshly as possible and grant full citizenship rights to freed slaves. After Lincoln's assassination, the Radical Republicans went on to pass a string of laws that would grant voting rights to freedmen, restrict any whites associated with the Confederacy from holding public office, create the South's first public school system, and provide charitable institutions like hospitals and asylums.

Answer 2

The Radical Republicans (a large group in the Republican-dominated Congress) thought that the government should be punishing the rebellious South, not helping it.