Why subscribe to printed versions of math journals?
Ok, as a paper fetichist, OA activist and former scientific advisor for a mathematical library, I cannot not answer this. But I must distinguish several perspectives.

What I like about paper journals

I like to hold them, and let the paper smell and nice typography sink in in the background of my mathematical immersion.

Unfortunately, most large commercial publisher are doing such an awful job that this emotion is barely possible anymore with many otherwise great journals. Come on: GAFA allows an article to start on a left page, in Advances you see both recto and verso superimposed because of the low-quality paper, even Inventiones has too light or too bold printing making papers sometimes difficult to read. Thank goodness there are still Acta with large yellow pages, the Annals, the journals of MSP and a few others that stand out, but unfortunately I lost my library when I got my current position.

I like that I get to know about what is done outside my fields

When I still had a great library with many paper subscriptions, I would look at all abstracts in certain journals, and when an abstract seemed interesting I would read the introduction. It would very rarely result in a direct connection to my own works, but I think I got several research ideas that way and more importantly, it would enlarge my mathematical culture constantly.

This point could be emulated in an electronic format (and is partially, through e.g. arXiv email alerts), but it is not the same at least for me, and in the current state of affairs.

I like the calm and solemnity of a library

I enjoyed very much to go from volume to volume following citations and knowing that I would get in a few minutes almost all I needed, while benefiting with the almost monastic atmosphere of a library. Being out of my office, this also meant no interruptions. 

This was only possible because the library I had was really great.

What are reasons to keep paper subscriptions outside of my own experience

To hold what we buy

For some time, electronic subscriptions gave permanent access to the period that was subscribed, but this seems to become the exception rather than the rule, and in any case might turn difficult to enforce (if you need a trial to get access, that is an issue). Once you buy a volume of journal, the publisher will not get in your library and take it back. There is a great safety in this, that electronic subscription cannot provide completely.

In France, we are devising a plan to have every significant mathematical journal identified and subscribed to by at least two libraries, in paper version, with a pledge to take good care of them (have them binded, indexed, etc.), mainly as a safety net.

Not much more

Honestly, the use of paper versions have declined so much that it is often difficult to argue in favor of paper versions, and I totally understand the choice to transform libraries into learning centers and concentrate on electronic subscription. It makes me a bit sad, but I get it.

One thing that has not been considered enough until now, is how to get electronic version better. They are still too close from scanned papers, which makes the situation far from optimal. My bet currently is that the energy needed to defend paper would be more useful in pushing for better public scholarly communication infrastructures (hat tip to Björn Brembs).