It is important to realise that languages change.
They change from period to period, from place to place and from one community or social stratum to another, while Hebrew is no exception.
Thus, the way Hebrew is pronounced in Brooklyn today is different from the way it was pronounced in Berdichev two hundred years ago, and both are different from the way it was pronounced in King David's times.
Moreover, there is even no sole Israeli pronunciation today.
Yemenite and Persian Jewry community members, Sephardic orthodox Jews and American immigrants, proud French-speaking minority and even Israeli Arabs - each one of these groups has its own pronunciation variants.
However, for the sake of convenience and simplicity the pronunciation of the current descendants of the Founding Fathers of Israel (which were mainly from the Russian Empire and other Eastern European countries) is considered to be the most representative, and it is what you are presented with in the following links.