Cicero was not assassinated, he was proscribed. The one was illegal and could result in prosecution for murder, the other technically legal, if abhorrent to decent Roman sensibilities. Shortly before Philippi the triumvirs enacted a series of proscriptions, in which Cicero was outlawed and executed. Plutarch believes that the very first proscribed consisted of a barter between the three triumvirs, each giving up one individual that they favored. Plutarch relates that Octavian gave up Cicero, Antony gave up L. Caesar (who was not in fact killed in the proscriptions), and Lepidus gave up Paulus. Following the execution of these (or rather, the two who weren't L. Caesar), Plutarch relates that the triumvirs proscribed three hundred more individuals. Appian's version of the first proscriptions is different. He says that the triumvirs drew up lists, starting with Lepidus who killed Paulus, then Antony who put L. Caesar on the list but later pardoned him, then the relatives of the consuls-elect, and so on. Before publication of the full list, Appian says, the triumvirs issued private orders that some twelve or seventeen of the proscribed should be killed in the night without official notice. Appian claims Cicero was on this short list, but that only four of the individuals actually were killed, and Cicero would not die until the second wave of proscriptions.

In any case, our sources are all pretty much in agreement about the reason for Cicero's inclusion on the proscription lists. That he was an opponent of Antony was noteworthy, but he was not the most hated of the proscribed. That distinction must go to Lepidus' brother Paulus and Antony's uncle L. Caesar, both of whom Appian tells us were placed first on the list because of their early opposition to their own kin. Plutarch and Suetonius both claim that Octavian, Cicero's protector, was reluctant to approve the proscriptions. No small amount of post-civil war Augustan rhetoric must surely be at play here, since both authors acknowledge that reluctant or not Octavian went about his work with great gusto once it began, but Plutarch's version is that it took three days for Octavian to allow Antony to place Cicero's name on the list of the proscribed, although Plutarch's certainty that Antony insisted that Cicero be placed at the head of the list is surely mistaken. Cicero, it is true, had been instrumental in Antony's fall from grace. After supporting Antony in his efforts to rehabilitate the conspirators and Caesarians Cicero had turned about-face and backed Octavian, eventually acknowledging his illegal private army with a grant, of questionable legality itself, of extraordinary proconsular power, despite Octavian's age and status. No doubt in reality Octavian was as happy to be rid of Cicero as Cicero would have been to be rid of him--the famous laudandum, ornandum, tollendum comment betrays that he thought of Octavian as little more than a pawn--but why Cicero in particular, when Cicero had proved himself willing, if reluctant, to retire from public life during Caesar's dominatio? Part of it must be the need among the triumvirs for money, a major factor in the proscriptions, and no doubt an equal part was due to their desire to eliminate all potential opposition, to which end they went to great lengths not only to remove dissent from outside of their circle but also combed the Caesarian ranks (interestingly P. Dolabella survived). But Plutarch and Appian are in pretty firm agreement that it was the Philippics that incurred Antony's hatred. Beginning on September 4, 44 Cicero, who had been essentially in retirement for several years and had only recently supported Antony, delivered a series of fourteen invective speeches (some of them probably only published and not spoken), some ad senatus and some ad populum against Mark Antony. The Philippics are Cicero's rhetorical masterpieces and easily his best invective. Firmly placing himself against Antony in a way that Cicero had only rarely opposed an enemy before he proceeded to soil his reputation so thoroughly that pretty much everything written about Antony's character afterward, despite Antony's attempts to control the situation through counter-pamphlets, was in some way a commentary on the Philippics. All that stuff about Antony being a drunk, or a womanizer, or a homosexual, or a moron, or deranged, or an enemy simultaneously of Caesar and the Roman people, or weak-willed, or any of it has its genesis in the Philippics, and by the time Plutarch wrote the Antony the contents of the Philippics had wholly overwritten everything else in the sort of "legend" that grew up around Antony, who was rehabilitated by some of the later Julio-Claudians, who were related to him. It's hard to understate what the Philippics did not only to Antony's political situation--the Fourteenth Philippic resulted in a successful vote to declare Antony hostis, a sentiment Cicero had already been expressing by the Fourth Philippic--but also to his reputation. Plutarch and Appian both relate that it was the Philippics in particular that roused Antony's ire--turning Cicero into what Syme called Antony's bête noire. From Plutarch:

τὴν δὲ κεφαλὴν ἀπέκοψεν αὐτοῦ καὶ τὰς χεῖρας, Ἀντωνίου κελεύσαντος, αἷς τοὺς Φιλιππικοὺς ἔγραψεν.

And he cut off his head and his hands, on Antony's orders, the hands by which he had written the Philippics.

And from Appian:

ἀπέτεμε δὲ καὶ τὴν χεῖρα, ᾗ τοὺς κατὰ Ἀντωνίου λόγους οἷα τυράννου συγγράφων, ἐς μίμημα τῶν Δημοσθένους.

And he cut off the hand by which he wrote the speeches against Antony, as if a tyrant, entitled in imitation of Demosthenes', the Philippics.

Fulvia of course had her own score to settle with Cicero, the result of a somewhat less successful invective campaign against P. Clodius

You have to understand the political context in order for Antony and Cicero to make sense. After the death of Caesar, Antony gathered an army and began to march against Caesar's assassins, who were also rightfully appointed (by Caesar) magistrates. Cicero read this action as a revolt against Rome and sympathized with the assassins who wanted to restore the regular workings of the Republic (read, the superiority of the Senate). We have many letters written between Cicero and the main conspirators: M. Brutus and Cassius, as well as several other men involved in this conflict including Lepidus, who would ultimately betray the Senate. For his part in the fight against Antony, Cicero led a major PR campaign against him writing pamphlets and delivering speeches in the Senate against Antony. He also supported Octavian who was, at the time, supporting the Senate's army led by the consul Hirtius and Panza.

Antony's army was forced into retreat at Forum Gallorum, but the consuls died in battle. This led to a power vacuum in Rome. Usually this would call for the appointment/election of a dictator who would hold power until another pair of consuls could be elected. However, before anything like that could happen, Antony retreated to Lepidus's camp and instead of pursuing them, Octavian, now in control of the Senate's army, joined them. Instead of appointing a dictator, they decided to have a vote that would allow the three of them special commands over different parts of the Roman empire as well as the powers of a dictator in Rome. This would last until they could restore peace by defeating Caesar's killers and Sextus Pompey who had been in revolt against Rome since the death of his father. The assumption was that once this was all over, they could give up their powers and the Senate would be restored (this had happened under Sulla, so it wasn't just a pipe dream).

This is wear politics became very important. These three men needed their government to be legitimate. They needed to present a united front. They needed money. Taking another note from Sulla they began proscriptions against their political enemies under the accusation of maiestas: treason. This was applied to people who acted against the state but it was applied very widely to include slanders against rulers and supporting the conspiracy against Caesar. Treason was a capital punishment and, uniquely, also a full forfeiture of property. It was used as a way to fund the triumvirate and to clear out political rivals. It also created a lot of empty seats in the Senate which could be filled with supporters of the triumvirate.

Based on those goals, Cicero was an ideal target for this proscription. His loud campaign against Antony would be silenced and his seat filled with a supportive youngster.

One of the issues with Antony is that he was slandered left, right, up and down at many points in his political career (as were most politicians). Antony found himself the victim of two major PR campaigns. The first was the one led by Cicero in the Philippics the second was one led by Octavian once the triumvirate disbanded. This painted him as a hedonistic tyrant of the Eastern (Persian/Hellenistic) mold and a threat to Roman values working against the quintessential Roman hero, Octavian. This second campaign was heavily influenced by Cicero and made his statements relevant again. You have to be careful about what you read about Antony. Much of the things said about him are boilerplate "bad guy" material that Cicero and others recycled over and over again. You can, for instance, compare material in the Second Philippic with Cicero's invectives against Piso in In Piso or Pro Sestio and descriptions of Catiline in Cicero and in Sallust. Think of it this way: what we have about Antony is like trying to make a history of Hillary Clinton using only material from the Obama and Sanders campaigns and conservative media.

I would recommend reading Plutarch's "Life of Antony." As you do, think about the kinds of things you have heard about Obama or Hillary in conservative media or about Senate Republicans in liberal media. What kinds of things does one side tend to say about the other regardless of personality (what have Obama and Clinton both been accused of separately)? What would Roman equivalents be? How do those things compare with the things said about Antony?