Although this is a little controlversial still, supposedly this has already been proven legal in court in the US. courts have determined that you can record the music you are entitle to listen to at home as "fair use" allowed under copywrite, so that youcan listen to it again later. This does not entain breaking an enryption scheme in any way. So it was actually included in a recent opinion as allowed fair use.
Then again, this could be a bunch of b.s. I was fed so that I though this was all OK, so YMMV, and I'm not responsible for what happens to you
1) The word is copyRIGHT, as in "the right to make copies".
2) The license granted to you as part of the terms-of-service of the subscription service explicitly denies you the right to make copies.
3) If you are in america, copying for the purpose of format conversion of items you have purchased, and continue to own, is _probably_ fair use, and that _may_ in the case of copy-protected media, invalidate the clauses in the DMCA that prevent it. This is untested in court so far, and curiously the media companies seem unwilling to let it be tested.
4) Point 3 does not apply to music obtained from subscriptions services as you haven't purchased that music, you are renting it.
If you are going to make assertions about copyright law, you really should know what you are talking about.
I am not a lawyer, although I have spent some time consulting with lawyers in this field, and you should not rely on anything other than point (1) above being accurate.