You can have a strong military response without authoritarianism. The Anarchist military during the Spanish civil war were formed from the bottom up: a group of soldiers elect their commander, those commanders collectively elect their general, etc, with any of those positions of authority able to be recalled by a vote (outside of battle) at any time if those elected positions weren't fulfilling their duties adequately.

This structure was doubted and questioned at the time by a military advisor to Durruti (an important Anarchist figure):

One day Pérez Farràs stated his criticisms to Durruti directly: “You can’t fight like that,” he declared. In reply, Durruti said:

I’ve said it once and I’ll say it again: I’ve been an anarchist my whole life and the fact that I’m responsible for this human collectivity won’t change my convictions. It was as an anarchist that I agreed to carry out the task that the Central Committee of Anti-Fascist Militias entrusted to me.

I don’t believe—and everything happening around us confirms this— that you can run a workers’ militia according to classical military rules. I believe that discipline, coordination, and planning are indispensable, but we shouldn’t define them in the terms of the world that we’re destroying. We have to build on new foundations. My comrades and I are convinced that solidarity is the best incentive for arousing individual responsibility and a willingness to accept discipline as an act of self-discipline.

War has been imposed upon us and this battle will be different than those we’ve fought in Barcelona, but our goal is revolutionary victory. This means defeating the enemy, but also a radical change in men. For that change to occur, man must learn to live and conduct himself as a free man, an apprenticeship that develops his personality and sense of responsibility, his capacity to be master of his own acts. The worker on the job not only transforms the material on which he works, but also transforms himself through that work. The combatant is nothing more than a worker whose tool is a rifle—and he should strive toward the same objective as the worker. One can’t behave like an obedient soldier, but as a conscious man who understands the importance of what he’s doing. I know that it’s not easy to achieve this, but I also know that what can’t be accomplished with reason will not be obtained by force. If we have to sustain our military apparatus with fear, then we won’t have changed anything except the color of the fear. It’s only by freeing itself from fear that society can build itself in freedom.

Source of that qoute.

That structure worked very well from all the historical evidence we have, and they were effectively able to fight the fascists with very few resources, until the combined weight of the stalinist's betrayal and Franco getting constant supplies from Hitler and Mussolini became too much to bear from a logistical point of view.

. Is it authoritarian to follow the commands of your captain when you are in battle?

If your whole life is a war, and you're living in military state, then sorry, but you're already in a way worst scenario than you think. Look at weird paramilitary groups that are using kids as a army, brainwashing is strong and they are saying what you said.

This is the problem with authoritarian stare. It steals your humanity and freedom, it thinks for you, and it control's you. It doesn't matter if you're slave of rulling class in capitalist stare or slave of rulling class in whatever you're referring to. It's the same state but with different flags and slogans.