Every time I read an RMS opinion, it seems to start at a good position and consistently attempts to be more and more idealistic to the point that he seems to be arguing a strawman.
RMS definitely is radical, but I've never known him to use strawman arguments.
I know he defines Malware differently from the common way (he considers DRM as malware, for example),
I guess he's also talking about backdoors for law enforcement (aka "legal interception") and other purposes.
but democratic values are less likely to be transmitted if I use Office? Proprietary developers want to punish students? I guess he means the corporations
His explanation indicates why he does mean proprietary developers rather than just corporations: e.g. in the US definition of core democratic values, there are aspects like personal freedom (e.g., modifying software) and the common good (e.g., sharing things with others). Note that he's not arguing here that it should be illegal for others to write proprietary software, i.e., he's not arguing to impinge on other people's liberty.
- and again, they don't generally give their source for modification, so they might be preventing students from modifying other people's work. Is that punishing them?
It limits the possibilities for expressing their creativity. Schools should be places where encouraging creativity is one of the highest valued goals. I know that is generally not the case right now (amazing video, btw), but this is a (small) way in which the situation can be improved.
I won't even claim to understand what the social mission of schools are supposed to be - prepare students for functioning in society?
I'm obviously not RMS, but I'd argue they should be prepared for functioning in society, for critically thinking about that same society (and anything else), and for contributing to a society that they consider to be better than what it is today.
Prepare them for jobs? Prepare them for college? Prepare them to develop free software?
I'd say: prepare them to become the best they can be. That can include a particular kind of job, being an artist, college (about which you can have very similar discussions as about school), developing free software or any combination of the above and many more things.
Prepare them for ignoring copyrights?
Now that last part is a great a strawman on your part: encouraging students to use Free Software, which they can share and modify freely according to the copyright license terms of that same software, is by no means the same as preparing them for ignoring copyright. It mainly teaches them that there are also alternatives to software whose business model depends on artificial scarcity. They will get to know MS Office and other popular products anyway, and if you can work with OpenOffice or LibreOffice, the jump isn't that great in any case. Maybe one of the primary things schools should teach are transferable skills (of which creative thinking is probably the "übervariant").