I think your question can go a long way towards answering itself. Tacitus refers to an emperor's role in one of the most devastating calamities Rome had seen. Tacitus is also held up as an exemplar for the best of classical historians (unlike e.g., Herodotus, whom even Thucydides mocked, or Diogenes Laertius, who wrote half biographies and half mythologies). It should be obvious that he wouldn't event some story about this fire unless there were one. So what else do we have? Almost nothing. We have Suetonius and Pliny and precious else to even tell us that this fire happened. Later historians, such as Cassius, weren't born until a century or so later.
So the answer to your question is "because there were almost no historians in the first century whose works survive even in fragmentary form". In fact, there weren't many historians at all, particularly if you discount those who, like the gospel authors, were fond of incorporating myth and legend into the "historical" accounts.
He disparaged them. He refers to Christianity as a "deadly superstition" which originated in Judaea, "the nexus/origin of this evil". He shows nothing but contempt for Christians and the founder whence came their name: Christ (whom he says was executed by Pilate).
Also, why would Christians quote him? We have evidence in Christian writings that pagans believed Jesus to be the product of Roman rape, that his followers were tainted atheists who should be executed, and that the entire foundation of Christianity is based on an executed criminal. We have no until the 18th century that anybody thought Jesus never lived. From Celsus through Julian, there were plenty of pagans who viciously attacked Christians in writing and whose works survive in whole or in part. There number of Christian responses/rejoinders is vastly greater. Yet nowhere did any Christian try to defend Jesus' historicity because nobody was challenging it.
Legion, provide evidence that Christians were even recognized as a distinct group apart from Jews during the mid-1st century or that "Christian" was even a widely used term back then.
Tacitus, Roman Politician and Historian, (c. 56-120 CE)
Turning next to another stalwart in the anemic apologist arsenal, Tacitus, sufficient reason is uncovered to doubt this Roman author's value in proving an "historical" Jesus. In his Annals, supposedly written around 107 CE, Tacitus purportedly related that the Emperor Nero (37-68) blamed the burning of Rome during his reign on "those people who were abhorred for their crimes and commonly called Christians." Since the fire evidently broke out in the poor quarter where fanatic, agitating Messianic Jews allegedly jumped for joy, thinking the conflagration represented the eschatological development that would bring about the Messianic reign, it would not be unreasonable for authorities to blame the fire on them. However, it is clear that these Messianic Jews were not (yet) called "Christiani." In support of this contention, Nero's famed minister, Seneca (5?-65), whose writings evidently provided much fuel for the incipient Christian ideology, has not a word about these "most-hated" sectarians.
...the Tacitean passage next states that these fire-setting agitators were followers of "Christus" (Christos), who, in the reign of Tiberius, "was put to death as a criminal by the procurator Pontius Pilate." The passage also recounts that the Christians, who constituted a "vast multitude at Rome," were then sought after and executed in ghastly manners, including by crucifixion. However, the date that a "vast multitude" of Christians was discovered and executed would be around 64 CE, and it is evident that there was no "vast multitude" of Christians at Rome by this time, as there were not even a multitude of them in Judea. Oddly, this brief mention of Christians is all there is in the voluminous works of Tacitus regarding this extraordinary movement, which allegedly possessed such power as to be able to burn Rome. Also, the Neronian persecution of Christians is unrecorded by any other historian of the day and supposedly took place at the very time when Paul was purportedly freely preaching at Rome (Acts 28:30-31), facts that cast strong doubt on whether or not it actually happened. Drews concludes that the Neronian persecution is likely "nothing but the product of a Christian's imagination in the fifth century." Eusebius, in discussing this persecution, does not avail himself of the Tacitean passage, which he surely would have done had it existed at the time. Eusebius's discussion is very short, indicating he was lacking source material; the passage in Tacitus would have provided him a very valuable resource.
Even conservative writers such as James Still have problems with the authenticity of the Tacitus passage: For one, Tacitus was an imperial writer, and no imperial document would ever refer to Jesus as "Christ." Also, Pilate was not a "procurator" but a prefect, which Tacitus would have known. Nevertheless, not willing to throw out the entire passage, some researchers have concluded that Tacitus "was merely repeating a story told to him by contemporary Christians."
Based on these and other facts, several scholars have argued that, even if the Annals themselves were genuine, the passage regarding Jesus was spurious. One of these authorities was Rev. Taylor, who suspected the passage to be a forgery because it too is not quoted by any of the Christian fathers, including Tertullian, who read and quoted Tacitus extensively. Nor did Clement of Alexandria notice this passage in any of Tacitus's works, even though one of this Church father's main missions was to scour the works of Pagan writers in order to find validity for Christianity. As noted, the Church historian Eusebius, who likely forged the Testimonium Flavianum, does not relate this Tacitus passage in his abundant writings. Indeed, no mention is made of this passage in any known text prior to the 15th century.
The tone and style of the passage are unlike the writing of Tacitus, and the text "bears a character of exaggeration, and trenches on the laws of rational probability, which the writings of Tacitus are rarely found to do." Taylor further remarks upon the absence in any of Tacitus's other writings of "the least allusion to Christ or Christians." In his well-known
Histories, for example, Tacitus never refers to Christ, Christianity or Christians. Furthermore, even the Annals themselves have come under suspicion, as they themselves had never been mentioned by any ancient author....
In any event, even if the Annals were genuine, the pertinent passage itself could easily be an interpolation, based on the abundant precedents and on the fact that the only manuscript was in the possession of one person, de Spire. In reality, "none of the works of Tacitus have come down to us without interpolations."
Regarding Christian desperation for evidence of the existence of Christ, Dupuis comments that true believers are "reduced to look, nearly a hundred years after, for a passage in Tacitus" that does not even provide information other than "the etymology of the word Christian," or they are compelled "to interpolate, by pious fraud, a passage in Josephus." Neither passage, Dupuis concludes, is sufficient to establish the existence of such a remarkable legislator and philosopher, much less a "notorious impostor."
It is evident that Tacitus's remark is nothing more than what is said in the Apostle's Creedto have the authenticity of the mighty Christian religion rest upon this
Pagan author's scanty and likely forged comment is preposterous. Even if the passage in Tacitus were genuine, it would be too late and is not from an eyewitness, such that it is valueless in establishing an "historical" Jesus, representing merely a recital of decades-old Christian tradition.
Pliny, Tacitus and Suetonius: No Proof of Jesus