Answer

A. Instead of asking how Abraham failed to bring me in as supporting evidence, ask why he didn’t bring all the halakhic and Talmudic sources.
B. Abraham went to war to save a relative of his. Are my life circumstances easier than his relative’s life? All the more so since apparently his relative also was not in mortal danger. On what grounds would he take me away from my studies to fight? In our case we’re talking about a war over all our lives. What does one have to do with the other? So objection A is resolved.
C. Where exactly do you see there that Torah protects and saves? Even if we don’t distinguish between Abraham’s war to save his relative and a war to save all of us — did anyone tell him that his relative would be saved without war by virtue of the learning? True, this whole principle is invented out of thin air, so you’re allowed to invent it here too.
D. Aside from the obligation, would there have been a desecration of God’s name there if they had not gone out?
E. Were those learners supported financially by Abraham? If so, then all the more so he was permitted to send them out, or to stop supporting them if they decide to devote themselves to Torah at his expense.
F. And we haven’t even talked about pressing into service Haredim who don’t learn, in which case Abraham certainly did not sin, Heaven forbid.
G. Now ask yourself why Abraham himself went out and didn’t stay in kollel. (After all, he certainly was a kollel avrekh whose Torah was his profession, and not just some Religious Zionist type or secular person, Heaven forbid. This requires further study. By the way, the state supported him quite nicely with all his cattle and sheep and camels. The kollel stipend there was excellent.
H. And all this is even if we take an obscure midrash that comes to convey some message through aggadah as a historical and halakhic source. I’m sure Abraham and those sharp young fellows in his kollel discussed this topic at length (when they weren’t going out to demonstrations against the state that doesn’t give them enough camels and doesn’t get itself killed enough for them).
I. And after all that, ask yourself how you yourself didn’t think of all the simple-as-an-egg arguments I wrote here. Perhaps the learning in your kollel is not really on such a high Torah level as one finds in hesder yeshivot? Or perhaps you too are busy dying in the tent of Torah (and not enlisting) instead of learning? By the way, apropos of Torah protects and saves: you can see it plainly. No Haredi in kollel who learns Torah has died in this war. A real tangible faith in the Torah outlook of the eyes of the congregation, who decree and the Holy One, blessed be He, fulfills. Fortunate are we, that every single moment we are stringent not to fall into forced labor (though a bit less stringent about actually being Torah scholars and not talking nonsense).