Why do you think Cassius and Brutus lost the war?

Judging from the information presented in Shakespeare's play, it would seem that Antony and Octavius have a distinct advantage from the time Brutus and Cassius ride "like madmen" out of Rome. Antony and Octavius have the power base in Rome, while Brutus and Cassius have to raise two armies and provide for them in the hinterlands. They stake everything on a battle at Philippi, and when they lost that battle they have lost the war. It would appear that Cassius, as usual, was right and Brutus was wrong. Cassius definitely did not want to fight at Philippi. In Act IV, Scene 3 he tells Brutus his reasons, as follows:

'Tis better that the enemy seek us;
So shall he waste his means, weary his soldiers,
Doing himself offense; whilst we, lying still,
Are full of rest, defense, and nimbleness.

By "nimbleness" Cassius evidently means maneuverability. But Brutus, as usual, overrules him.

Good reasons must of force give place to better.
The people 'twixt Philippi and this ground
Do stand but in a forced affection,
For they have grudged us contribution.
The enemy, marching along by them,
By them shall make a fuller number up,
Come on refresh'd, new-added, and encouraged;
From which advantage shall we cut him off
If at Philippi we do face him there,
These people at our back.

Cassius tries to interrupt:

Hear me, good brother.

But Brutus is characteristically sure he is right:

Under your pardon. You must note beside
That we have tried the utmost of our friends,
Our legions are brim-full, our cause is ripe:
The enemy increaseth every day;
We, at the height, are ready to decline.

Here Brutus concludes his argument with some of Shakespeare's most famous lines:

There is a tide in the affairs of men
Which taken at the flood leads on to fortune;
Omitted, all the voyage of their life
Is bound in shallows and in miseries.
On such a full sea are we now afloat,
And we must take the current when it serves,
Or lose our ventures.

These famous words are important because they apply to all of us. There is a tide in most of our lives which would lead us to success if only we recognized it as such and took advantage of the opportunities it offered. Unfortunately, many of us do not recognize these golden opportunities until after we have failed to take advantage of them. Shakespeare was apparently thinking in terms of tides because there were only certain times to embark from England on the Thames, which was strongly influenced by ocean tides. When the incoming tide filled the river, that was the time to embark on important ventures. The ambitious voyager would have deep water and a strong outgoing tide to carry his sailing vessel out to sea.

Cassius and Brutus would not have been in their critical position if Brutus had not overruled Cassius when Cassius wanted Antony to be assassinated along with Caesar. Then they would not have been in their inferior position if Brutus had not magnanimously permitted Mark Antony to speak at Caesar's funeral--much against the wishes of Cassius. Shakespeare makes that famous funeral address pivotal. It forces Brutus and Cassius to flee from Rome. They might have survived longer and even prevailed if Brutus had not insisted on fighting Antony and Octavius at Philippi. Shakespeare makes it seem that Brutus was at fault for the loss of the war.

In Act V, Scene 1, Cassius confides his forebodings to his aide Messala:

Be thou my witness that, against my will,
As Pompey was, am I compell'd to set
Upon one battle all our liberties.