Interesting about your class, I had some of the same discussion in some of mine (not film school, MBA stuff). I even had to do a breakdown of Netflix's future prospects (my group thought it would be dead soon, I disagreed).
Things about physical media
Yes, it can take up space on a shelf. But then, you can copy it to a media player and put that disc/box into a closet. The shelf life for a professionally pressed disc is really not known yet, if handled properly. Having that disc mitigates against drive failure that kapoofs all your movies.
Assuming your friends and/or family have a DVD or Blu-ray player, you can just take your disc over and pop it in. It would be a little bit more cumbersome to take your media drive over. Even, say, if you had it on your laptop, will they have the correct plugs to watch the film from your laptop?
There is still confusion among the studios as to what versions of media get what extra features. Right before Blockbuster went down, it was using a special disc that came with no features, mainly to deter the sell-through aspect of previewed movies. (Aside- which I find pretty damn stupid since I have never heard/read a single person rave about the special features of a rom-com movie. Action films, sort of. But sci-fi and horror I hear about all the time.) I'll discuss this more under the digital section.
Cool objects. Why do people buy neat box sets, such as the Terminator Head, the Phastasm Ball, or the Tomb of the Blind Dead coffin? Because they are awesome collector's items. Why do some people plates that feature former Presidents? Yes, they are insane, but they think they are collectible. People, in general, but getting less so with the younger generations (hell, I have to use the damn plural now), like to have something. Why do we take pictures? To have a solid memory of that moment. Inside, we know that at some point, our memory of that moment may fade, just like a digital version of something may falter.
And, if you no longer have LPs, and zombies attack, you can use your DVD/BR discs as weapons.
Things about digital media
Takes up no physical space, can copy all day long, limited only to your drive space. Sounds great, everything you want. But not quite. The vast majority of people do not routinely, if at all, back up their drives. Depending how you got your digital film, this may or may not be a problem. Some distributors will let you re-download the file, some won't. So you either get a redo or you repay. If you got a torrent, you can probably get it again. Generally torrents will not have any extra features, and be of lesser quality (so I have been told). Plus, there is always that threat of a lawsuit over your head.
Going back to the special features item. As the AwesomeSimitar has already pointed out, different digital versions have different special features. Which as I noted above, doesn't really seem to bother most people, but then again, we are not most people. Also, the whole concept of digital distribution is in a very complex state of flux right now; just look at what Netflix has been doing the past couple of months. Look at how the studios are trying to squeeze Netflix for more money just for the "honor" of hosting their content. Then throw in cable and satellite TV with their OnDemand content. This whole digital service model is nowhere near being settled.
I haven't touched on DRM (Digital Rights Management) yet. For actual discs, all you need is to buy a program to strip it away (Monkeys nor HM neither condone nor condemn such actions). Streaming media is a bit more difficult. Newer cable boxes, TV, and DVD/BR players are incorporating HDCP over HDMI (copy protection over those new fancy cables) to make sure you can't copy a signal in-between. Yes, it can be gotten around, but it is more difficult than ripping a disc (Cthulhu and Bobo neither condemn nor condone such actions). But this leads us to….
Vendor lock in. For example, Amazon has a digital movie rental and purchasing store, which is good. What is bad, though, is that purchased movies are DRM'd so they films can only be watched on Microsoft PCs. Yes, there is a way around that, too (nope, not doing it again). So I bought "Necessary Roughness" (Manu Manu the Slender!), and can't play it on my Mac. Various set-top boxes, TVs, and B-R players have various connections to online distributors (Hulu, Amazon, Netflix, Pandora, etc), but you can't upgrade the devices or add new distributors.
Final word on digital media- it is still being worked out in the marketplace.
Thoughts of a Monkey
I wanna a banana.
Physical media is going to be with us for a long time yet. Manufacturers are already looking at ultraviolet laser discs. Holographic storage is actually progressing, albeit slowly. The main difference between vinyl, 8-tracks (HA!), cassettes and optical media is that optical media is always backwards compatible. CDs used a laser, DVDs used a smaller wavelength laser, B-Rs used an even smaller wavelength laser. Smaller bandwidths can read bigger channels in older discs.
The other problem is that real broadband in the US (sorry to exclude my foreign brethren here, Hollywood and all) is spotty and fairly crappy compared to many parts of the rest of the world. Yes, it is much better than many other parts of the world, too. But until we have fibre or DOSCIS 3+ going to at least to the suburbs of cities, pure digital media is not going to take over 100%.
So, physical media is around for at least another 20 or so years. Digital media will keep making inroads, drive space will keep getting cheaper, and distribution channels will start to figure out what they are doing. Digital media will gradually replace physical media, but I doubt that physical media will ever be totally displace.