We need to remember that in Shakespeare's day, a lot of importance was given to dreams and signs such as Calphurnia talks about. This is a strategy that is used by Shakespeare in Macbeth as well to suggest nature revolting against a seismic event that will happen that it profoundly wrong: the murder of a leader. Of course, as sagetrieb identifies, the true tragedy of this section of the play is how easily Caesar is manipulated by Decius into going to the Senate after he has decided to stay at home for the day. Caesar shows himself to care more about honour and glory than the wishes of his own wife, and his underestimation of her wisdom and sensitivity to omens leads to his downfall and death.
Some might call Calphurnia superstitious, and indeed the play is full of superstition, which Shakespeare’s audience respected as did Romans in ancient times. Others might call such sights and dreams with which she warned her husband to stay home that day as a form of intuition manifesting itself through dreams—such as hers about a statue and blood, or sights—“a lioness hathe whelped in the streets, / And graves have yawned and yielded up their dead” (2.2.17-19). And maybe its not the truth of these claims that is at stake, but rather her love for her husband and the means she will use to protect him. Certainly, had he listened to her, the play (and history) would have been different. He did not listen to her because he did not want to appear weak to the senators, and so in this sense his pride trumped his respect and love for his wife, and compelled him to go to the senate and meet his fate. So at core her reasoning is "I love you; indulge me in my fears no matter how silly they might seem to you; please stay home today," and I do think Caesar,as many husbands, might be more successful if they took more seriously the concern of their wives and loved ones.