Why does Caesar decide to go out even though, he has been warned by the Soothsayer and Calpurnia?
Note the other answers concerning Caesar's vanity, his arrogance, his over-confidence. Decius knows precisely which buttons to push. On the other hand, perhaps this is the day that Caesar will die, no matter how he tries to avoid his fate. Consider how many other times fate seems to play a role: Cassius dies on his birthday, Antony's prophesy about the "dogs of war" comes true, Caesar's ghost appears twice to Brutus, Cassius sees the prophetic eagles replaced by scavanger birds.
My point is that it is not hard to explain Caesar's actions in light of his personality; his character flaws. On the other hand, as with many of Shakespeare's plays, fate seems to have a controlling hand as well. In that case, Caesar fatefully goes to the Capitol because he must.
In Act 1.2, the Soothsayer (one who predicts the future) twice warns Julius Caesar, "Beware the ides of March." He has foreseen that on this date, March 15, Caesar will meet a grim fate. Caesar does not listen to him, nor to the warnings of his wife, Calpurnia, who also senses that danger looms. Caesar's decision to ignore both the Soothsayer and Calpurnia speaks to his hubris (excessive pride, presumption and/or arrogance) will be his undoing. Though he "doth bestride the narrow world like a Colussus), he is also "spoiled by success and adultion" (Homer Watt).
Here are the lines in which he spurns the Soothsayer (1.2.25-26):
Beware the ides of March.
He is a dreamer; let us leave him: pass.
Caesar's pride is his undoing and tragic flaw, and it is this that prevents him from staying at home. Decius, knowing that Caesar's pride is his weakness, uses it against him, reinterpreting Calphurnia's dream to mean that men see Caesar as great and revere him and come to him for aid and support and wisdom, and telling Caesar that if he does not go to the Senate that day, then he will be thought of as a coward and that the senate will refuse to give him the crown they had intended to give him that day, and that pricks another of Caesar's flaws, his ambition, for he wants to be crowned emperor.
Confidence and arrogance! Caesar has already named himself Dictator for Life, he is on the verge of being crowned king, and has just defeated the mighty Pompey - what does he have to fear? Remember that:
"Danger knows full well
That Caesar is more dangerous than he,
We are two lions littered in one day,
And I the elder and more terrible."
Act 2.2 44-47
Anyone who feels like that shouldn't be scared of bad dreams and silly omens!
Julius Caesar, is a man of strong will. He is very courageous and ambitious to the core. He had no belief in superstitions and was ready to face any challenge. The nightmare which Calpurnia had seen and the warning of the soothsayer had no impact on Caesar.He says that danger and himself were born toether and he is the elder. He claims danger itself knows how Caesar is more superior to it.