Describe the irony in the following lines found in Act 3, scene 2 of the play, Julius Caesar: "Good countrymen, let me depart alone. And, for my...

The irony lies in the fact that, without realising it, Brutus is setting the stage for his eventual downfall. By asking the crowd to allow him to leave on his own and not follow him and thus listen to Antony's oration, he creates an opportunity for Antony to inflame the crowd and turn them against the conspirators.

Brutus completely underestimated Antony's ability or desire to incite the citizens against him and his fellow conspirators. After they had murdered Caesar, Antony came to ask permission to speak at Caesar's funeral. Brutus was quite agreeable to this, much against the much more suspicious and cynical Cassius' advice. In an aside he told Brutus:

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?

Brutus replied:

By your pardon;
I will myself into the pulpit first,
And show the reason of our Caesar's death:
What Antony shall speak, I will protest
He speaks by leave and by permission,
And that we are contented Caesar shall
Have all true rites and lawful ceremonies.
It shall advantage more than do us wrong.

Cassius was keenly aware that Antony could say things which could culminate in a citizen's riot against them but Brutus naively believed that if he set terms on how Antony should address the crowd and protest against whatever is inappropriate, there would be no danger. This adds to the later irony after he had addressed the crowd since he does not have the opportunity to protest because he leaves when Antony takes the podium.

Brutus informs Antony:

Mark Antony, here, take you Caesar's body.
You shall not in your funeral speech blame us,
But speak all good you can devise of Caesar,
And say you do't by our permission;
Else shall you not have any hand at all
About his funeral:

As it so happened, Antony followed Brutus' instructions to the letter and repetitively referred to the conspirators as honourable men, each time after he had mentioned one or other of Caesar's virtues. The crowd soon caught on that Antony was mocking the conspirators so-called honour by repeatedly contrasting their actions with Caesar's virtues. His cleverly constructed speech soon had them baying for blood. The crowd who had, just moments before, supported Brutus were now intent on destroying him and all the other plotters.  

Antony slyly stayed the crowd, asking them to wait until he had read Caesar's will. He wanted to drive them into a frenzy so that they were completely overwhelmed by a lust for vengeance. Once he had read the favourable terms of Caesar's will, they had become so worked up that they became unstoppable and as seen as Antony concluded his speech, they went on the rampage, hunting down and tearing to pieces whoever they believed had been involved in Caesar's brutal assassination. 

The unfortunate Cinna the poet became a victim of the citizen's savage retribution and he was torn to pieces even though he mentioned that he was not a conspirator. The crowd, however, had been overwhelmed by an overriding bloodlust and he was killed for 'his bad verses.' As for Brutus and his partners in crime, they all fled the city, fearing for their lives.