The Hebrew people spoke Hebrew in Jerusalem, not aramaic. That is historical, biblical fact.
If you mean they spoke Hebrew and not Aramaic in the time of Christ, its a total falsehood. Hebrew was by the time of Christ spoken only in a liturgical context. The names of Jewish people at the time of Christ prove this to be the case, as do the last words of our Lord before His death and resurrection as recorded in the Synoptics, and His other words.
There are three examples that provide proof that Galilean and Judaean Aramaic was the language predominantly spoken by our Lord and the people of the Holy Land during His lifetime:
- Bar Abbas - in Hebrew this would be Ben Abbas, for Ben means Son, which is Bar in Aramaic.
- Mark 5:21-43 records our Lord miraculously reviving, resuscitating or resurrecting an unresponsive 12 year old girl believed to be dead (Since our Lord said she was sleeping, I am not certain if this was a resurrection, like with Lazarus, but it could have been). This account is also found in Matthew 9 and Luke 8, but in Mark, the words our Lord actually spoke are recorded, “Talitha cumi.” This is Aramaic meaning “Arise, little girl” (the word Talitha is one of endearment and can also mean “lamb”).
- On the cross, our Lord quoted Psalm 22:1 but did so in Aramaic, “Eli, Eli, Lama Sabacthani?” This, being translated is My Lord, My Lord, why hast Thou forsaken me? In Hebrew, in which Psalm 22:1 was composed by King David, to the tune Hind of Dawn , which is sadly lost, like the rest of the original music of the Psalter, the opening verse “My Lord, My Lord, why hast Thou forsaken me?” is transliterated as Lam’natzayach al-ayeles hashachar mizmōr l’dovid.
So obviously, unless you were talking about Jerusalem prior to the Babylonian conquest, possibly well before, such as during the reign of King Solomon and his successors, before the Northern Kingdom was conquered by the Assyrians, which would have resulted in an influx of Aramaic speaking refugees (probably Levites), merchants and diplomats, from then until Nebuchadnezzar invaded, it should be obvious that Aramaic was spoken by the Jews in Jerusalem, and by the time of Christ, it was spoken even in some parts of the Synagogue service (for example, the Targumim, which were Aramaic translations and interpretations of the Hebrew scriptures).
Pilate had Jesus' "crime", for which He was crucified, written in 3 languages,
HEBREW,
Latin,
and greek,
and nailed to the cross for all who passed by to read.
In Hebrew, all the Hebrew speaking, reading people passing by read the tetragram of His crime which spelled
Y
H
V
H.
it made the priests furious, and they complained to Pilate and asked him to change it.
Pilate said: "What I have written, I have written."
Ok, firstly, not sure where you are getting that story, since that’s not what the Bible actually says. Lets open up John chapter 20:
21 Pilate also had a notice posted on the cross. It read:
JESUS OF NAZARETH,
THE KING OF THE JEWS.
20 Many of the Jews read this sign, because the place where Jesus was crucified was near the city, and it was written in Hebrew, Latin, and Greek.
21 So the chief priests of the Jews said to Pilate, “Do not write, ‘The King of the Jews,’ but only that He said, ‘I am the King of the Jews.’”
22 Pilate answered, “What I have written, I have written.”
Now that being said, Pilate may well have had it written in Hebrew, which many literate Jews could read, but spoke only in the synagogue or in the Temple. It was a liturgical language, and indeed had been for many centuries, most likely since at least the Persian conquest of Babylon (even before that time, however, Akkadian was dying among the Mesopotamians in favor of Aramaic, just as Sumerian had been displaced by the Semitic language Akkadian many centuries before, and just as many centuries later, Aramaic would be displaced by Arabic, another Semitic language).
Regardless of whether it happened prior to, during or after the Babylonian Captivity, this change to Aramaic as the vernacular language is why parts of the Old Testament are written in Aramaic, including substantial portions of Daniel and Ezra.
This resulted in a phenomenon wherein Greek and Roman literature commonly referred to both Hebrew and the Aramaic dialects used by the Jews, Old Testament Aramaic, Galilean Neo-Aramaic and Judean Neo-Arwmaic, as Hebrew, except in those rare cases when there was a need to know exactly which language was being referred to (St. Jerome’s writings concerning his translation into Latin of the Old Testament from the Hebrew and Aramaic text, to replace the original second century Latin Bible, which was translated from the Septuagint, the Greek translation of the Old Testament).
This makes a great deal of sense, because both Hebrew and Aramaic were written using the same alphabet, and because the Imperial Aramaic alphabet had been superseded in Syria and Mesopotamia by what would become the Estrangelo script in which the Syriac Aramaic translation, Bible, the Peshitta, was written, starting with the Old Testament in the second century and finishing with the New Testament in the fourth century (with 5 books omitted from the initial translation, 2 John, 3 John, 2 Peter, Jude and Revelation, translated by the Syriac Orthodox by the 6th century).
Indeed, even in the early 1700s, Harvard University boasted of its prowess in teaching future Congregationalist ministers Greek and Hebrew, so they could read the Holy Bible in the original languages. But of course, in their Hebrew curriculum were courses on Aramaic, because of the various parts of the Old Testament, not limited to Daniel and Ezra, but even occurring in Genesis in the Masoretic text which was used by the Protestants exclusively until the 20th century for translating the Old Testament.
Around the same time that Aramaic became the vernacular language of the Jews, Imperial Aramaic script was adapted to replace Paleo-Hebrew as the primary form of writing Hebrew, and this modified “Square letter script” remains in use to this day. Indeed, the Jewish diaspora in Europe expanded its use, writing the Yiddish dialect of German in Imperial Aramaic, as well as the Sephardic Judaeo-Spanish dialect Ladino. And even though Hebrew has been restored as the language of Israel, because nearly all Jewish literature whether written in Hebrew, Old Testament Aramaic, ancient Judaean Aramaic, Talmudic Aramaic, certain Jewish Aramaic dialects spoken by small communities in Syria and the Holy Land prior to the formation of the State of Israel, Yiddish, or Ladino, is written in Imperial Aramaic.
Only the Samaritans continued using a form of Paleo-Hebrew, the Samaritan script, in which Samaritan Hebrew, Samaritan Aramaic, and Arabic are written. However, some Dead Sea Scrolls written in Paleo-Hebrew dated from 100-200 BC have been found, suggesting a small community of Jews did try to preserve their ancient text, and this community I suspect probably lasted until some time between the destruction of the Temple in 70 AD and the Bar Kochba Revolt in 130 AD, events which led to the Essenes, Sadducees, and other Jewish denominations disappearing, so that among the former people of Israel, only the Rabinnical Jews, Ethiopian Jews and Samaritans survived (and later, the Karaite Jews would rebel against Rabinnical authority and were at one time quite numerous, even converting a Crimean tribe, the Khazars, who have since largely reverted to Paganism, in order to avoid persecution by the Nazis and the Soviet Union; this led to hatred for and discrimination against Karaite Jews in general, even though the Karaites living in Israel are from Alexandria and Syria, and are ethnically Jewish, unlike the Khazars of Crimea.