This question keeps cropping up, and whenever it does, people claim it was their language. The question needs to be precisely framed. Oldest spoken language in the world? All equally old. Oldest still spoken language in a particular area? It's easier to answer this for islands or archipelagos, e.g. Great Britain: Welsh. New Zealand: Maori. Japan: Ainu (but maybe not for much longer). Oldest written language? Sumerian…
Hebrew never ceased to be used in liturgy and in religious studies - the same situation also holds true for Coptic, so the oldest written language still spoken (in religious capacity only) is Coptic.
But Hebrew was also used as a lingua franca between different Jewish communities all over the world. This was not a minor role, and it had quite an economic impact on forming long-range trade networks across Jewish communities.
Now there are more things people might love to argue about, such as when we can really define a script as "writing" and how do we deal with undeciphered scripts. So one can try to discredit Proto-Canaanite inscriptions like Wadi el-Hol or claim that ancient Chinese pottery symbols that are precursor to Oracle bone script are actually related. The evidence seems to be stronger on the Hebrew side, but it's very easy to derail this kind of argument just to score national pride points.