Is supporting Sci-Hub illegal/unacademic? In the classroom, one of the students asked me about Sci-Hub. I answered that I like the idea as I am against the tyranny of publishers. As a fun fact, I added that I have even donated to Sci-Hub.

Then, I received a notice from our department head referring the case to the disciplinary committee since Sci-Hub is illegal and any direct and indirect support of an illegal activity is against the university policy.

Is supporting Sci-Hub illegal / unacademic?
In my view it is foolish to describe Sci-Hub itself as illegal. Acts can be illegal, but not "things" or groups of people. Only activities. While it is true that they may engage in illegal activities, that is not the same thing. 

However, if what they do is copyright infringement (very possibly) then you can't participate in that. 

However, if you want to upload things for which you hold copyright to Sci-Hub or a similar site then you aren't engaging in any illegal activity, nor is any downloader, provided that you grant an appropriate license. 

Countries and other jurisdictions make laws. People (and organizations) can break those laws, but the people themselves, and the organizations do not themselves become illegal. 

I think your university is right to open a disciplinary hearing only if you advocate breaking laws to students. 

I agree with you that publishers have put a lock on science and culture that is very unfortunate. Especially when copyright no longer seems to expire after a reasonable period, and fair use is losing ground. Publishers are transferring what should be a common good into a private profit making enterprise. They are, IMO, stealing from the public. If you can afford not to give them copyright on things then I encourage it, but the whole system has made it hard for academics to build a reputation otherwise. Long term this tends to make us dumber, not smarter. As they say: Sad. 



I'll add an historical note. There was once a valid reason for publishers to want to hold copyright on articles they published. There was a lot of friction (read cost) between an author and a potential reader. As such, since the publisher bore a lot of the cost (not the creation cost, of course), they needed assurance that they could recoup what they spent in making scientific articles available - especially since the material itself had value, but the number of potential readers was small (relatively speaking). 

But that world is now long past. Publishing is nearly frictionless now. Publishers can still provide a useful review (done by volunteers) and editing (done by paid professionals) function, but the distribution cost is near zero and borne partly by users in any case (internet fees). Most of the real cost of the creation of publishable material today is borne by the author, by universities and scientific organizations, and by government. Publishers in the old model are an anachronism if not an oxymoron.