LF: Maybe you can call it whatever you want and maybe you thought it up yourself, but that doesn’t remove the offense at all. A very comparable case would be going up to an African-American, calling him the n-word, and then excusing it by saying that you didn’t mean any offense and you were just using a variation of the Latin word for “black”. See how well that goes for you.
To respond to the actual discussion of whether the day is one worthy of celebration, everyone agrees that many of the “founding fathers” of the State had Yiddishkeit nowhere near their minds. In fact, many wanted to be rid of traditional Yiddishkeit. No one disputes that. There were also those involved who did it because they wanted to be able to fulfill all of the Mitzvos as HKBH commanded us and to bring all Jews back to Eretz Yisrael.
All that aside, though, nothing comes from man. Dati Leumi and other Frum people don’t celebrate Yom Ha’atzma’ut because some people (Frum and not) signed a document in 1948. It is celebrated because, in 1949, almost the entire Jewish world because commemorating that day as a day of tremendous Chasdei Hashem where, not only did He give us a safe place where we can practice Yiddishkeit as we were meant to, but He also clearly showed us an absolute early sign of the coming Geulah BB”A.
You are attacking a straw man. You have decided that Yom Ha’atzma’ut is a man-made holiday and therefore should not be compared to holy days. But it is not a man-made holiday. At least, not for the Frum. For the Frum who celebrate it is an acknowledgement that Chazal said there is a Chiyuv Min HaTorah to make a Yom Tov (not Yontif as in Asiyas Melacha, but a Yom Tov as in a good day), replete with the saying of Hallel, whenever HKBH does a Nes for all of Klal Yisrael that serves as a function of heralding a Geulah and Binyan Beis Hamikdash.
Now, I am not saying it’s Muskam that all of the assumptions required to get to the logic in the last paragraph are Muchrach. I would be willing to admit that Ruba D’ruba of the Olam does not hold of all of that, and a large Rov doesn’t even hold of most of it. But don’t come tell me that there is nothing at all Jewish about it. There are many who have a Mesorah, from Moshe Rabbeinu at Har Sinai, that includes it, in the exact same manner that it includes Channukah and Purim. (Well, almost the exact. Chazal had the Koach to mandate with absolute terms that those days were an Aschalta D’Geulah and therefore Leis Man D’palig that they should be celebrated. We nowadays have to work with assumptions and we admit that, therefore, we could be wrong. Butt we’re not making it up on our own. We firmly believe that this falls into the parameters of making a Yom Tov.)
Oh, and a certain R’ Ovadia Yosef, among many others, would disagree with your contention that there is nothing Jewish at all about the day (though he is certainly not happy about those who say Hallel). See Yabiya Omer OC 5:35 and 6:41, if I recall correctly.