Why the Radical Republicans wanted to impeach President Johnson and why Reconstruction failed.
The stated reason for the impeachment proceeding against President Johnson was that he had fired a member of his cabinet without the consent of the Senate, in violation of Federal law. Years later, that law was found to be unconstitutional.
But the real reason was that the Radical Republicans did not trust Johnson. He was a Democrat running a Republican Administration because of the death of Lincoln. He did not support the Radical Republican agenda which involved putting punishing terms on the southern states, continuing to rule them through military dictatorship, and giving new civil rights to the former slaves. Radical Republicans believed that without these policies the the Civil War victory would be compromised by allowing the South to return to its old ways.
I wouldn't say that Reconstruction failed. It's primary purpose of bringing the Southern States back into the Union as loyal States that would never again rebel proved quite successful. But another important goal for many, allowing former slaves to become full citizens with equal rights under the law, did not take hold. The former slaves did have some rights under the military governments that ruled during Reconstruction. They could vote, run for political office and had other basic rights, they and their descendents lost most of these rights in the years after Reconstruction ended. Southern whites simply refused to treat blacks as full citizens or to allow them any power or rights.
Northerners after more than 12 years of reconstruction and 4 years of war decided they could not continue to force the south to submit to northern policies against their will. Controlling southern states by military dictatorship ran afoul of the democratic policies on which the US was founded. Once southern whites were able to elect their own leaders again, many of the civil rights gains for blacks were reversed. While slavery could not be reinstated, blacks began to live in a State of virtual slavery, forced to work as share croppers under burdensome debts that they could never repay. The right to vote was taken away via various requirements such as literacy tests or poll taxes. Blacks seeking reform were often intimidated or killed by extra legal groups such as the KKK which operated with tacit local government approval. As a result it would be another century before real reform would come to the south.
I hope this helps!