Why did Superman risk his life in the final fight?

Examining the psychology of Superman in this telling of his story gives us a strong answer.

Remember that throughout this movie Superman has faced criticism and doubt as to his character, presence, and purpose. Faced with this existential pressure he is visited by his father in a dream and it is precisely during this dream that I believe he receives the "nugget" of wisdom that produces the action we see in the end. His father tells him the story of having saved his family's farm only to have condemned the neighbors farm to destruction in the process. The message is a bit murky but one thing is clear: with any victory comes sacrifice.

Superman already feels much guilt over his failure to stop the bomb in the capitol and is also frustrated with the world's accusations that he is at fault for the deaths of all those connected with the Metropolis incidents. Now, facing another Kryptonian foe, he understands one gigantic lesson that will lead to him becoming the Superman that many are familiar with: self-sacrifice. If he wants to save everyone else, it must be him that receives the full weight of the cost of that victory. Or said another way: To prevent the destruction of the neighbor's farm, he must destroy his own.

Could he have given the spear to another? Maybe. Could he have thrown it? Maybe. There is only one way to be absolutely certain the beast falls, however. He must put the spear through its heart himself, regardless of personal cost. Thus, his decision was one of idealism, and heavily influenced by the previous events of the story.

Because he didn't have the time to plan tactics. They were fighting with a monster (Doomsday), that is much stronger and more powerful then they are. In order to give the kryptonite sword to Wonder Woman, he has to convey this whole plan to her first and she was barely able to fight with Doomsday. She was not free for a single moment and Batman was just surviving. So he can't take the risk of extending the fight, otherwise Doomsday could reach a highly populated area and kill many civilians. So Superman just took the opportunity to eliminate this threat, even though his conversation with Lois proved that he knew the risk.

One point also to be noted that Superman was nearer to the spear and he was quite weak as compare to his original strength, so throwing will give a chance to miss.

The spear not only had to hit Doomsday, but it required Superman piercing him and the spear coming out the other side, which takes considerable force. Throwing the javelin could have missed and in his weakened state would not have the necessary force to inflict enough damage. Also Doomsday was emitting large waves of energy that would have further bungled an attempted throw.