Another plausible explanation of Marc Antony's request that he be killed by Brutus is Antony's clever manoeuvring; for he is confident that the noble Brutus will not murder him since he realizes that Cassius may have already advised Brutus to assassinate him, but Brutus cannot simply kill Antony and then credibly explain that the assassination of Julius Caesar has been purely to prevent tyranny and was a noble act.

By asking Brutus to kill him, Marc Antony hopes to dispel Cassius's assessment of him as dangerous since he is "so apt to die"

No place will please me so, no mean of death
As here by Caesar, and by you cut off,
The choice and master spirits of this age

and to set Brutus up for his request to speak to the Romans and camouflage his intentions to turn the plebeians against the conspirators.

In William Shakespeare's Julius Caesar (III,i), Antony asks (beseeches) Brutus to kill him. While Antony does not truly wish to die, he recognizes the gravity of the situation facing him (Brutus and the conspirators have just murdered Caesar). 

Antony states the following when asking to die:

If I’m going be killed, there is no time like
Caesar's death-hour, or any instrument
Half as worthy as your swords, decorated richly
With the most noble blood in this whole world.
Please, if you hate me, kill me now
While your purpled hands smeared with fresh blood.

1) Antony believes that if he is to die, there is no better time to die than the same hour his king has died. He looks upon Caesar with great respect and believes that it would be an honor to die as close to his king as possible. 

2) Also, Casear's blood is upon the swords which would take Antony's life. He, again, finds it honorable to die by the same sword which took the life of Caesar. 

3) Lastly, Antony does not wish to live if those around him hate him. He believes that if they hate him, it would be better for him to die. 

Overall, Antony provides readers with numerous reasons why Brutus and his fellow conspirators should kill him. Luckily, Brutus refuses to kill Antony ("Beg not your death of us").