Why does Caesar want Calpurnia to stand in Antony's way in Julius Caesar?

Caesar wants Antony to run by Calpurnia so that she will be given fertility.

During the Feast of Lupercal, Antony is taking part in a ritual in which he will run naked through the streets.  He is able to do this because he is very fit, and a solider.  He is also considered an example of fertility. (Antony had many children). 

CAESAR

Stand you directly in Antonius' way,
When he doth run his course. Antonius!

ANTONY

Caesar, my lord?

CAESAR

Forget not, in your speed, Antonius,
To touch Calpurnia; for our elders say,
The barren, touched in this holy chase,
Shake off their sterile curse. (Act 1, Scene 2)

Caesar is hoping that some of Antony’s fertility will run off on Calpurnia, his wife, because Caesar and Calpurnia have never had a child. (Caesar had a daughter from a former marriage).  It is a Roman superstition that the men who participate in the race can grant fertility to any woman they hit with their leather strap.  Antony would have been expected to hit many women along the course.

The race is part of an overall celebration that Caesar has co-opted.  Even though it is a religious holiday, he is using it as part of his victory route.  Brutus and Cassius do not like this, and the general excitement the crowd has shown for Caesar, so they do not participate.  Brutus also tells Cassius why he is not running the race.

BRUTUS

I am not gamesome: I do lack some part
Of that quick spirit that is in Antony.
Let me not hinder, Cassius, your desires;
I'll leave you. (Act 1, Scene 2)

Brutus is essentially saying he is not athletic.  Shakespeare takes this opportunity to contrast Brutus and Antony.  Antony is strong, athletic, and fertile.  Brutus, on the other hand, is lacking in pretty much all of these areas.  It foreshadows Antony’s later domination of him.  The Roman people preferred shows of strength.  By running the race, Antony is also ingratiating himself to the people of Rome.

The incident at the race also highlights aspects of both Caesar and Antony’s characters.  Caesar is domineering and authoritative.  He has no qualms about calling attention to what appears to be his wife’s infertility.  In fact, he has to.  Since they have no children and he has to put on a show as a virile man, the fault has to be hers.  Antony, for his part, is immediately obedient and says, “When Caesar says 'do this,' it is perform'd.”  It is indicative of their relationship, and also demonstrates how Antony wants to tie himself to Caesar—and his popularity with the people.