/u/ghostofherzl and /u/gingeryid (under a previous alias) have previously answered In the lead up to and when Israel became a nation, how did people develop an effective social and political state when everyone spoke a different language; or was modern Hebrew already spoken by the majority?
/u/hannahstohelit has previously answered
More answers remain to be written.
An Israeli here, very happy for your interest, and glad to add my two cents (or shekels).
So, what is Yiddish? Yiddish is regional Jews language that was spoken in religious Jewish communities in Eastern Europe in the 500 years, it is very similar to German, though the alphabet is like in Hebrew.
why Yiddish wasn't chosen to become the official language of Israel?
1.It was a languages of religious communities. The whole idea of Zionism (The idea of Jewish nationalism) was the rise of Jewish unification based on nationalism in contrary to religion. The Yiddish language rejected because it was religious and popular among the less educated people that founded Israel.
Why Hebrew?
3.Speaking in Hebrew was prohibited because it was a sacred language spoken only in synagogue during praying. The Zionist movement implicitly wanted to create a Jewish nationalism, and they wanted to pull the religion out.
The idea of coming back to the land of Israel (then, Palestine, some still regard it Palestine) was integrated with speaking the languages of our forefathers, Hebrew.
Hebrew alphabet and many words were known to jews via religious praying and it was easier to make it Hebrew.
Important note:
Hebrew was also debated and, many people wanted German, French or English to become to formal language of Israel, Hebrew took them over because of some jews intellectuals that reinvented the languages, built dictionaries and publish newspapers.