Why does Brutus choose to commit suicide at Philippi in Julius Caesar?

Choice A is the correct answer: To ancient Romans, suicide was an honorable way to die if it helped one avoid defeat and humiliation.    
 In Ancient Rome, suicide was considered an honorable alternative to being humiliated by the enemy.  Brutus and Cassius did not want to be captured by Antony and Octavius and marched in triumph through Rome.  A triumph was a military parade where the victor showed off his spoils and his captives.  It would have been the ultimate defeat for Brutus and Cassius. 
Before the battle, Brutus and Cassius discuss their plans if things go wrong.  They do not plan to be Antony’s captives.  This is a civil war.  To be marched in their own city as captives is unthinkable. 

CASSIUS
Then, if we lose this battle,You are contented to be led in triumphThorough the streets of Rome?
BRUTUS
No, Cassius, no: think not, thou noble Roman,That ever Brutus will go bound to Rome;He bears too great a mind.  … (Act 5, Scene 1) 

What do you do then?  If victory is out of grasp and it looks like there is a certain defeat, Brutus and Cassius agree that they will kill themselves.  In fact, each of them do.  Cassius thinks that he sees his enemies surrounding his men, when in fact it is a victory celebration he sees. He commits suicide prematurely, on his birthday. 
Brutus commits suicide later, when he knows that all is lost. 

… Countrymen,My heart doth joy that yet in all my lifeI found no man but he was true to me.I shall have glory by this losing dayMore than Octavius and Mark AntonyBy this vile conquest shall attain unto.So fare you well at once; for Brutus' tongueHath almost ended his life's history … (Act 5, Scene 5) 

Antony later calls Brutus the noblest Roman of them all.  He believes that unlike some of the other members of the conspiracy, Brutus was not involved for fame or power. He really was doing what he thought was best for Rome.