The Semitic Language Tree chart represents a variety of Semitic language scholars opinions.
As with anything, the scholarly community is not 100% agreed.
Please notice that Eblaite is listed in both the Eastern and Western Proto-Semitic lines. This is because Eblaite has both elements linguistically. The more that is uncovered archaeologically, the more the linguists have to work with in determing linguistic families. Also, Jewish is differentiated from the Hebrew. Hebrew represents the pre-exilic, first temple time period. During and after the exile, Aramaic and Arabic had more influence on what came to be known as Jewish or Modern Hebrew.

Before anyone starts crying foul, you need to do some research into the subject.
Hebrew was no longer a spoken language, but a liturgical language,in the same way that Latin was
for much of the later Catholic Empire. The majority of those attending mass did not know what the priests were reading and saying in Latin, which was not their spoken tongue.

Eliezer Ben Yehuda, a Jew born in Lithuania in 1858, was a Jewish activist for a homeland for the dispersed Jews. He realized that there was no way a homeland would be achieved without a spoken, written language. He is considered the father of Modern Hebrew.
"As he (Ben Yehuda) suggests, if it were true that Hebrew was, in fact, no different from the classical languages of antiquity, then, 'Let us revive the Hebrew language,' for, in this way, Hebrew would become useful to the younger generation, instead of being '...a dead language...not useful for anything'...'We can only revive the Hebrew language in a country where the number of Jewish inhabitants is greater than the number of Gentiles. Let us therefore increase the number of Jews in our desolate country, place the remnant of our nation in the land of their forefathers, and thus we will revive the nation, and its language too will live.' "

Upon arriving in Palestine in 1881, Eliezer wrote, " 'There was no common language...for all the Jews living in Jerusalem. The members of the different communities spoke the languages and dialects they had used in their mother countries or in their fathers' homelands. The Sephardim (Mediterranean and Middle-Eastern Jews) spoke Judaeo-Spanish..., the Musta`arabin (local Jews) spoke Palestinian Arabic, the Maghrebines (North African Jews) Arabic according to the North African dialect, the Caucasians spoke Georgian, the Crimeans Tatar and the Ashkenazim (European Jews) spoke Yiddish in different dialects. Arabic was the language of the street common to all city dwellers who dealt with work and trade, but when the learned men from the different communities met together, they would speak among themselves Hebrew according to the Sephardic accent.' " "The type of Hebrew used by these people was, however, quite bookish and artificial and was generally reserved for discussions centered around the study of a Holy Text." Palestinian Hebrew was the Hebrew that Yehuda adopted to purify, making it the national Hebrew. In his work with resurrecting Hebrew, Ben Yehuda borrowed heavily on Aramaic and Arabic for current language, especially technical subjects, such as math and the sciences. The above quotes are from The Revival of a Classical Tongue; Eliezer Ben Yehuda and the Modern Hebrew Language, Jack Fellman, Bar-Ilan University, Israel, 1973.