As an amateur Talmudist, I like to understand both sides of arguments.
The draft debate as I see it:
In the view of the pro-draft party [the vast majority of the country] there are not two sides. There is only one side. Charedim MUST serve. This is not opinion but fact. It is as debatable as the sky being blue or that fat people weigh more than skinny people or that black people are better athletes than white people.
But - in fact, it is NOT fact. It is based on a number of beliefs. Everything people believe is based on other beliefs they are usually not even conscious and aware of.
The beliefs:
1] Hashem doesn't want Yeshiva boys not serving. Maybe they are correct. Hashem doesn't engage in direct communication with me so I can't know for sure. But either do they know for sure. Many claim not even to believe in Hashem but that is also a [completely unprovable and unfounded] belief.
2] They believe that learning Torah and keeping mitzvos properly doesn't help us in our war effort. That is a belief that they can't prove.
3] They believe that in a Democratic society, it is OK to forcibly conscript people into the military. Again - a belief with which one can argue.
The Dati Leumi community agrees with the general, secular community on point one. They believe even more: That Hashem actively WANTS Yeshiva boys to serve. Point two some buy into and don't believe in the power of Torah and mitzvos [רח"ל!!] and some do believe in the power of Torah in mitzvos even at war. But they say that even though Torah and mitzvos help, it must go hand in hand with army service [as per the army of Dovid Hamelech etc. etc.]. Point three they agree with. They believe that it is perfectly legitimate in a free democratic society to forcibly conscript anyone you want.
The Charedi position is also based on a belief system:
1] Hashem wants Yeshiva boys in Yeshiva and not in the army. They can't prove it absolutely [b/c, frankly, there are sources that point in the opposite direction besides the sources that point in that direction] but they believe it.
2] Torah study is a critical part of the war effort. It helps no less and even more than RPG's. This is a belief based on many psukim in the Torah and Maamarei Chazal. It can't be denied - if one believes in Torah [which of course nebuch the secular do not nor do some in the Dati Leumi community].
3] They don't believe in a Democratic society. Their allegiance is to G-d and G-d alone.
So we see that even though people on both sides frame this as being a no-brainer [in favor of their side] it is not so simple. It is based on beliefs that neither on both sides can prove mathematically. I like to think that both sides mean well even though one side is obviously wrong [and I have my own opinions which side that is].
The Charedim say that this is Torah and understandably not negotiable. The other side feels that the Charedim are immoral. Thus we are in the midst of a verbal civil war which is escalating from day to day. This services our physical enemies and the spiritual כחות הרע which feed upon our divisiveness.
ה' עוז לעמו יתן ה' יברך את עמו בשלום!!!
