1. The survival of the Jewish people is at stake. Learning Torah is more important. Even if Israel were “driven into the sea”, we would survive because there are Jews throughout the world learning Torah. We’ve been through a lot a tight situations, and the single theme in Jewish history is that Torah and Mitsvos is the key to survival.
2. The IDF is very hostile to Orthodox Jews. In fact, a large percentage of Shomer Shabbos Jews who serve do so only in segregated units where their frumkeit is tolerated, but where they are discriminated against in terms of job assignments and promotions. In general, it is very hard for Orthodox Jews to function in a secular environment in which Shabbos and Kashruth are at best tolerated, and where pritzus is a social norm (which is why some rabbanim poskened the army has a din of a Beis Busha – a view supported by widespread complaints among hiloniiot of sexual harassment). There is also the fact that the IDF has historically seen its job as “modernizing” (a polite way of saying “secularizing”) people in creating a modern secular state – which has great significance by halacha since if you are in a situation where non-observance is being coerced for reasons of undermining yiddishkeit, one is required to have mesiras nefesh even over trivial things (the traditional example is over how one ties one shoes). That means a frum soldier will end up being in a situation of having to give up on mitsvos, or openly oppose orders in an institution where there is seriously “frowned upon”.
3. Some frum Jews question the legitimacy of the State of Israel. If one bases the Jews’ claim to Eretz Yisrael on Torah, you have the problem that it was clearly given for the purpose of doing mitsvos. If there is no halachic basic for the state founded by Hertzl and Ben Gurioun, how it is mutar to kill (or be killed) in defense of that state, noting that in “modern” warfare a soldier often has no control over who he kills. In most western countries, someone with such views would be a conscientious objector and would be exempt from military service – but for Israel to accept such a view as legitimate would be admit that it is a question whether the State of Israel has a valid claim to the Jewish legacy pertaining to Eretz Yisrael (and perhaps it is, as the Arabs claim, an Euro-American ultra-secular colonial regime, and no more).