Heck Tate's first and foremost duty was to protect Boo Radley. But because Atticus seemed convinced from the outset that his own son committed great crime and was ready to see him fairly tried. I think a secondary reason for Heck to present this argument was to protect Jem. Obviously Jem was a victim, but knowing Ewell was dead, Atticus jumps to conclusions about how it was done. I think Atticus comes to believe that there was a struggle that resulted in Jem's injury, but that Jem was the victor who actually took the life of Ewell. Tate, knowing better than to incriminate himself or Boo tried to keep quiet and not discuss much with the ever-moral and just attorney Atticus. Atticus would have acted on the evidence trying to do the morally right. Tate has to leave him with the "let the dead bury the dead this time Mr. Finch."
I believe that Heck Tate does this because he does not think that it would be right to expose Boo Radley to a trial. He thinks that it would be like shooting a mockingbird.
I also think that Heck Tate sort of thinks that Bob Ewell had it coming. He feels that Ewell caused Tom Robinson's death and he is probably pretty unhappy about Ewell attacking Scout and Jem.
So between those two things, Tate feels that there is more justice in calling it an accident than in going after Boo Radley.
In the book To Kill a Mockingbird Heck Tate has to be insistent because Atticus believes that his son, Jem had killed Bob Ewell.
Atticus finds that he can not live with himself or his son if he says one thing and does another so he states he wants his son to stand trial if he had killed Bob. He is really fixated on the fact that his son had killed him.
Heck Tate knows that Boo had stabbed Bob, but to get Atticus to let go of the notion of Jem killing Bob he has to be adamant with Atticus. In addition, he is aware that if Boo goes to trial he will not get a fair trial because people will not be any different towards Boo than they were towards Tom and another innocent man will be harmed.
Tate believes that Bob already had it coming to him but if they expose Boo to a court right away then this will ruin the justice that happened because he saved the children. Boo is like a mockingbird who is innocent and if he is subjected to court then this will ruin him. Atticus was planned on going to court and resolving this but Tate finished what he was saying and just let it be.