In "To Kill a Mockingbird", why would Atticus want Jem to take the blame for the murder of Mr. Ewell or Bob Ewell?
Following Bob Ewell's attack, Sheriff Tate confirms that Bob died after falling on his own knife. However, Atticus does not believe Sheriff Tate and assumes that Jem is responsible for murdering Bob Ewell after listening to Scout's description of the attack. Atticus tells Sheriff Tate,
If this thing’s hushed up it’ll be a simple denial to Jem of the way I’ve tried to raise him. Sometimes I think I’m a total failure as a parent, but I’m all they’ve got. Before Jem looks at anyone else he looks at me, and I’ve tried to live so I can look squarely back at him . . . if I connived at something like this, frankly I couldn’t meet his eye, and the day I can’t do that I’ll know I’ve lost him (Lee, 277).
Essentially, Atticus believes that Jem should take responsibility for murdering Bob Ewell because it is the morally right thing to do, and he fears that his children would have a negative perception of him if he were to cover up Jem's involvement in the murder.
Throughout the novel, Atticus has tried his best to teach his children how to behave with honor and integrity. If Atticus were to lie about Jem's role in Bob Ewell's death, he would be doing his son a disservice, and his children would view him as a hypocrite. Atticus initially wants Jem to take the blame for Bob Ewell's death for the same reason he chose to defend Tom Robinson. Atticus simply wants to be able to live with the choices he makes in life and to have his children view him as a man of integrity. Eventually, Sheriff Tate indirectly tells Atticus that Boo Radley was responsible for Bob's death, and Sheriff Tate then explains why he refuses to inform the community of Boo's heroics. After listening to Tate's reasoning, Atticus accepts the fact that Sheriff Tate is doing what is best for their reclusive neighbor.
It's a matter of owning up to one's deeds, whether they are justifiable or not. Atticus does not want Jem to grow up with this great cloud over him, so to speak, with people around him staring and talking behind his back. He doesn't want anyone to ever have the chance to say that Jem got away with anything, as a trial will most undoubtedly bring about a verdict of non guilty due to self defense. By owning up to what he has done now, early in life, Jem will save himself years of people wondering what really did happen. Atticus wants everything to be in the open, so that truth can prevail and set his son free.
Atticus is most concerned with Jem's personal accountability. He doesn't want his son growing up with some kind of dark past that people are constantly talking about either directly or behind his back.
By using his knowledge of the legal system, he begins to formulate ways that Jem could easily escape charges, like the plea of self-defense. However, Sheriff Heck Tate assures Atticus that Bob Ewell "fell on his knife," despite evidence that Boo Radley stabbed him in defense of the Finch children.