This is a spin on the fact that he was a participant in the murder of Caesar. Cicero was trying to take back power that had been lost to a very popular Leader by participating in the murder of said leader.[0] The killers and conspirators involved were all hunted down and killed.
[0] - for those not up on Roman institutions, Dictator had a different role than we would ascribe today, albeit with many similarities.
Cicero was killed because Antony had a personal vendetta against Cicero. Antony's political partner, Octavian, had a good relationship with Cicero and even looked on him as a father figure. Giving him up to Antony was a compromise he was very unhappy to make (but Antony was not flexible on this demand).
Cicero, if anything, is an example of how one can be loud and open with their thoughts and actually get along well with political leaders (and he got on well with Caesar as well, supposedly). His murder is primarily indicative of Antony's pride.
The Equites were purely a social/wealth based class, any Roman citizen could become one if he we satisfied the wealth requirements.
However, the Senatorial class was not an economic distinction either but rather an aristocracy. Even in the Late Republic these were old families who had had Senators and Consuls in their heredity. There were fewer of these clans, 14 at the time of Caesar (of the Julii clan). Cicero by comparison was of Equestrian rank and a New Man, novus homo, in the Roman political world.
Equestrians weren't knights anymore, expected to field a horse, .... The Roman legions had been professionalized by then. There were property and suitability requirements enforced by the Censors.
The important point is that no one should mistake the equestrians for anything close to even the top end of the middle class.
He loved the Roman Republic and it's senatorial grandeur, and hated Caesar for his illegal arrogation of power.
Another triumvirate was formed after the death of Caesar with Anthony, Octavian and Lepidus. The proscriptions were from that triumvirate and not just Anthony. Cicero favored Octavian but as future emperor, Octavian favored Octavian. Antony certainly hated Cicero and Octavian didn't find Cicero all that useful and well, that was that.