What were the four disagreements Cassius and Brutus had in Julius Caesar?

Cassius and Brutus disagreed about swearing an oath, killing Mark Antony, letting Antony speak, and Philippi.

Cassius is the one who invited Brutus to join the conspiracy.  He needed Brutus for his name and reputation. Brutus had a reputation for being noble, and he would lend legitimacy to their cause.  They would need legitimacy once what they did had been discovered.  However, Brutus was not content to be a figurehead.  He wanted to be in charge and make the decisions.

The first disagreement Brutus and Cassius have is at the first meeting of the conspirators. Cassius brings everyone in and introduces them to Brutus and then wants them to swear an oath.  Brutus immediately overrules him.

No, not an oath: if not the face of men,
The sufferance of our souls, the time's abuse,--
If these be motives weak, break off betimes,
And every man hence to his idle bed;
So let high-sighted tyranny range on,
Till each man drop by lottery. (Act 2, Scene 1)

Apparently, if you are in a conspiracy with Brutus you are in it. He will not accept any paltry oaths.  Anyone who betrays them is “guilty of a several bastardy.”  That’s that.

The next big argument is about who should die besides Caesar.  Cassius is worried about Mark Antony, but Brutus tells him that Antony will be no trouble to them.  He is not dangerous without Caesar.  He should either kill himself or go into the woodwork.    Brutus is very adamant about not killing anyone other than Caesar.  He wants to make sure people think of them as “sacrificers, but not butchers.”

The next disagreement is an important one.  Standing over the body of Julius Caesar, Brutus and Cassius debate whether Antony should be allowed to speak at Caesar’s funeral.  Antony asks politely if he can speak, and Brutus consents.  Cassius is concerned.  He tells Brutus he does not think it is a good idea.

You know not what you do: do not consent
That Antony speak in his funeral:
Know you how much the people may be moved
By that which he will utter? (Act 3, Scene 2)

Cassius seems aware that Antony is a shrewd and cunning soldier.  Brutus is in way over his head.  He thinks that Antony is just in mourning for his former mentor, but Antony is planning a coup.  Cassius clearly sees how Antony can use his speech to gain power by turning the people against them, but Brutus believes what they are doing is noble and he thinks the people will take his side.

Even after the disaster with Mark Antony, Brutus still does not listen to Cassius.  The last time he ignores his advice is over the issue of Philippi.  Brutus and Cassius and their armies are on the run for their lives from Antony and Octavius, but Brutus chooses to go to Philippi. Cassius thinks the move is a bad one strategically.

'Tis better that the enemy seek us:
So shall he waste his means, weary his soldiers,
Doing himself offence; whilst we, lying still,
Are full of rest, defense, and nimbleness. (Act 4, Scene 3)

Brutus doesn’t listen.  He wants the upper hand so badly that he doesn’t realize he is making a terrible mistake. He does have doubts though.  He imagines the ghost of Caesar, a mixture of his doubts and guilt, telling him that he will see him at Philippi.  Brutus is doomed, and Philippi will be his doom.

Cassius has more leadership and military experience.  Why does Brutus never listen to him?  The answer lies in Brutus’s own arrogance.  He tries so hard to be honorable in all of his actions that he completely loses sight of reality.  He sees the world through a naïve lens, and although he has Cassius for guidance, he never listens to him.  Even though not taking Cassius’s advice results in disaster time and time again, Brutus continues.