AIC: Rav Schachter quotes a Chassam Sofer that there’s an Issur of Ba Tosif to make an extra hoiday. How, then could Chazal have made Channukah and Purim? The CH”S answers that there must be a Passuk or a Makor that one must make a holiday on a day which leads to a Geulah having to do with the Binyan or upkeep of the Beis Hamikdash/Eretz Yisrael. Rav Schachter also quotes Rav Herzog who quotes a Ramban that when Jews control Eretz Yisrael a third time they are Muvtach from HKBH that they will never lose it again. That is the source for celebrating Yom Ha’atzma’ut. Because it is a day that is remembered as being part of the Geulah, because HKBH has now promised us that we will never lose Eretz Yisroel again. Interestingly, Rav Schachter points out that no such Havtacha exists on keeping Yerushalayim. Thus, according to Rav Schachter, there is far more reason to celebrate Yom Ha’atzma’ut than Yom Yerushalayim.
As an aside, one of the most fun Gematriyos I’ve heard in my life is that Yom Ha’atzma’ut has the same Gematria as Bittul Torah.