All Jewish Sects. including Christians, were immersed in the Larger Greek culture of the period , “Hebrew was a older regional language rarely used
This conception of Hellenism implies a definition of “Hellenistic Judaism.” All the varieties of Judaism in the Hellenistic period, of both the Diaspora and the land of Israel, were hellenized, that is, were integral parts of the culture of the ancient world. Some varieties were more hellenized than others—that is, some were in more intense contact with non-Jews than were others—but none was an island unto itself. It is a mistake to imagine that the land of Judea preserved a “pure” form of Judaism and that the Diaspora was the home of adulterated or diluted forms of Judaism. The term “Hellenistic Judaism” makes sense, then, only as a chronological indicator for the period from Alexander the Great to the Maccabees or perhaps to the Roman conquests of the first century BCE. 
Diaspora Jews did not speak ny Semeitic languages
The essence of hellenization, of course, is the Greek language; the root meaning of the verb “to hellenize” is to speak Greek, or to speak Greek properly. In the Diaspora, the triumph of the Greek language was complete. Hebrew was virtually unknown to Egyptian Jewry. Even Philo, certainly the most learned and literate Jew produced by the Jewish community of Alexandria, was no Hebraist; in all likelihood his knowledge of Hebrew did not extend beyond select words and phrases of the Torah. Elsewhere in the Diaspora, the situation was the same. Virtually all the inscriptions engraved by Diaspora Jewry, from Egypt to Rome to Asia Minor, were in Greek. In Rome, a few were in Latin, and a few epitaphs append the Hebrew word shalom, but again there is no sign that the Jews of these places spoke or knew any Semitic language. The earliest literary work produced by Diaspora Jewry was a translation of the Torah into Greek, known as the Septuagint (third century BCE). By the second century BCE, the Jews of Egypt were writing scholarly essays, philosophical tracts, and poetry based on this Greek translation. As far as we know, Greek was the exclusive language of literary expression for Diaspora Jewry.
Even in Palestine, Jews and Gentiles both relied on Greek ( and Aramaic )
In the land of Israel, the situation is much more complicated because Greek had to compete with Hebrew and Aramaic, but even here many Jews spoke and wrote Greek. The Maccabees arranged for the translation of 1 Maccabees from Hebrew into Greek (this translation survives; the Hebrew original has completely disappeared). A Jew from Jerusalem translated the book of Esther into Greek. The Wisdom of Ben Sira, a work written in Hebrew by a sage around 200 BCE, was translated into Greek by the author’s grandson. By the first century CE, if not before, Judean authors like Josephus and his archrival Justus of Tiberias were writing original compositions in Greek. Greek documents have been found at Qumran and constitute a large part of a private family archive that was discovered in the Judean desert and dates from the first quarter of the second century CE (the Babatha archive). Bar Kokhba wrote some of his letters in Greek. In the burial caves at Beth Shearim in lower Galilee, which were in use during the third and fourth centuries CE, most of the epitaphs are in Greek, although most of the inscriptions of contemporary synagogues are in Hebrew and Aramaic.
Even in rabbinic circles, the Greek language had an enormous impact. This is evidenced not only by the thousands of Greek (and Latin) words in the rabbinic lexicon and by the fact that in a synagogue of Caesarea in rabbinic times the Shema was recited in Greek, but also by the fact that some rabbinic Jews needed a Greek translation of the Bible
To what extent Hebrew was a spoken language in Judea in Second Temple and rabbinic times remains a disputed question. It is likely that many of the people used Aramaic.
Its unclear how much of the Bible was actually written in Hebrew rather than Greek or Aramaic, and later translated into Hebrew ( a religious literay language much like Latin in the Church )
By the fourth or third century BCE, it became a literary language for the Jews (Dan. 2–7, Tobit, and Enoch were written in Aramaic) and would so remain until the Middle Ages.
Note that ancient Hebrew overlapped almost entirely with larger, older Gentile language systems that predated the existence o Israel
The first major discovery connecting the Phoenician alphabet and language with Hebrew occurred on January 19th, 1855, when Turkish laborers accidently uncovered an ancient sarcophagus in Sidon, a Phoenician city. On this sarcophagus was a lengthy inscription written in the Phoenician alphabet and language, which was found to be identical to Hebrew with only a few exceptions.
Old Hebrew Discoveries 
Figure 7 – Sarcophagus found in Sidon with Phoenician inscription 
The sarcophagus bears a 22 line inscription, known as KAI-14, written in the Phoenician Canaanite language, in the Phoenician alphabet. The inscription identifies the king inside and warns people not to disturb his repose.
Figure 8 – Meshe Stele inscription 
The inscription is by far the most important yet found in Palestine. It has added essentially to the scanty knowledge of the history and religion of Moab itself, and has thrown light on the fortunes of Israel east of the Jordan, as well as upon the foreign relations of the dynasty of Omri. The character of the language of Moab is also pretty fairly indicated.
In regard to the last point it may be noticed that the inflections depart but very seldom from those of classical Hebrew. The masculine plural ends in “-in” instead of “-im,” and there is an ifte’al verbstem. “Waw” consecutive with the first person imperfect is regularly followed by the cohortative or subjunctive. The vowel-letter ה is used for the pronominal suffix of both genders.
The Meshe Stele, also called the Moabite Stone, was discovered in 1868 in the Biblical city of Dibon, the capital of the Moabites. The inscription was written with the same letters as the Phoenician, old Hebrew and Samaritan and it was discovered that Moabite language was also the same as Hebrew with some minor variations. 
“Hebrew” in the Bible refers to the Canannite language (then Phoenician ) or sometimes Aramaic 
Hebrew is The language of Canaan” (and Moab)
The designation “Hebrew language” for the language in which are written the Old Testament …The same designation is frequently used by Hellenistic authors to denote the Aramaic language spoken at a later time by the “Hebrews,” as the Jews were called by non-Jewish writers. In Hebrew literature the term is first met in the Mishnah (Yad. v. 4; Giṭ, ix. 8); Biblical writers use the expression “the language of Canaan” (Isa. xix. 18) or “the Jews’ language” (II Kings xviii. 26, 28; comp. Isa. xxxvi. 11, 13; Neh. xiii. 24; comp. also the modern use of “Yiddish”).
The Hebrew language might be appropriately called the Israelitish dialect of Canaanitish, a branch of the Semitic Languages spoken in Palestine and in the Phenician colonies. Almost identical with it is Moabitish, as seen in the stele of Mesha (See Moabite Stone). Closely akin to it was Phenician, and in all probability also the languages of Ammon, Edom, and Philistia. The language used in the Zenjirli inscriptions approaches Hebrew closely.
Originates as a local dialect of Aramaic~Arabic
n the Middle Ages it was a prevailing opinion that Hebrew was the primitive speech of mankind. This view was based on “etymologies and other data in the early chapters of Genesis [comp. Berliner, “Beiträge zur Hebräischen Grammatik,” p. 9; König, “Hebräisch und Semitisch,” pp. 113 et seq.], which, however, were as plausibly turned by Syriac writers in favor of their own tongue” (“Encyc. Bibl.” ii. 1987; comp. Audo, “Syriac Dict.” Preface). A similar opinion was expressed by Rab (Sanh. 38b). Medieval Jewish scholars considered Arabic and Aramaic, the only cognate languages known to them, as corruptions of Hebrew. In more recent times, however, two opposing theories have been held. One, whose chief exponent is S. D. Luzzatto, is that Hebrew is derived from Aramaic; the other, whose chief exponent is Olshausen, is that it is derived from Arabic. D. S. Margoliouth (“Lines of Defense of Biblical Tradition,” and “Language of the Old Testament,” in Hastings, “Dict. Bible,” iii. 25 et seq.) claims that Hebrew is nothing but a vulgar dialect of Arabic. 
Arabic preserves more of proto-semitic than other regional languages 
Roots of the Arabic Language
As I mentioned above, Arabic is descended from a language known in the literature as Proto-Semitic. This relationship places Arabic firmly in the Afro-Asiatic group of world languages. Merrit Ruhlenís taxonomy in his Guide to the Worldís Languages helps to further elucidate Arabicís ancestry within this large group of languages. Specifically, Arabic is part of the Semitic subgroup of Afro-Asiatic languages (293). Going further into the relationship between Arabic and the other Semitic languages, Modern Arabic is considered to be part of the Arabo-Canaanite sub-branch the central group of the Western Semitic languages (323). Thus, to review, while Arabic is not the oldest of the Semitic languages, its roots are clearly founded in a Semitic predecessor.
Arabic as a Proto-Semitic language
As mentioned above, Arabic is a member of the Semitic subgroup of the Afro-Asiatic group of languages. The common ancestor for all Semitic languages (i.e. Hebrew or Amharic) in the Afro-Asiatic group of languages is called Proto-Semitic. Based upon reconstruction efforts, linguists have determined many of the phonological, morphological, and syntactic features of Proto-Semitic. As might be expected, not all Semitic languages have equally preserved the features of their common ancestor language. In this respect, Arabic is unique; it has preserved a large majority of the original Proto-Semitic features. In fact, many linguists consider Arabic the most ëSemiticí of any modern Semitic languages in terms of how completely they preserve features of Proto-Semitic (Mukhopadhyaya 3-4).
- MOABITE STONE:, Jewish Encyclopedia
- Eshmunazar II [ Sidon Phoenician~Hebrew ] sarcophagus
- The Ancient Hebrew Alphabet
- Hebrew lanugauge, Jewish Encyclopedia
- A History of the Arabic Language, Brian Bishop, Linguistics
- From the Maccabees to the Mishnah, by Shaye Cohen