Echoing the "You'll get lots of different answers" reply.

My personal experience was that I needed to listen to tango music, specifically, for two reasons:
1.
To like it. Sure, you can learn all about abstract musical structure from any music, or I suppose even from books or phone apps. However, tango has a very specific gamut of instruments played according to a small range of peculiar styles to create particular harmonies, according to compositions intended to be danceable using tango steps first and agreeable to listen to second. For quite a while, I found it to be charmless music – a horrific din that reminded me of the music my grandfather played through a horn from wax cylinders (he was born in 1899). Exposure to tango, the music as I studied tango, the dance led me to understand
why it sounded like it sounded, and eventually to appreciate it as music.
2.
To be ready for it. Tango is an improvised dance and you should never dance a tango the same way twice, much less choreograph it, unless you're
actually choreographing for performance. However, there are only about 150-200 tangos out of all the thousands that exist that you'll hear all that often. Knowing that core œuvre from the first few notes lets you invite someone, or choose to accept or decline an invitation from someone, on the basis of whether you like the music and/or feel that's the right person to dance that music with. It also lets you avoid being stuck dancing an energetic piece that starts deceptively slow, or vice versa, or an intense piece that starts deceptively light, or vice versa, at moments when your energy or focus isn't suited to it.
These days, all that listening I did means that I can dance reasonably well to a totally unknown piece, or to live music by playful musicians, because I know the structures and the surprises that tango music supports. Some people here will claim that those things aren't unique to tango, but are general musical principles. I can only respectfully disagree with them.
But I still listen to tangos when I work on boring, repetitive tasks, or cook, or mix cocktails, or host a dinner party with tango friends, because now I actually
like to listen to them! Especially with other tango people, when conversation trails off, knowing which era of what orquesta with who on piano (or whatever) provides an instant subject of discussion.
(Edited to add: All of the above assumes that most milongas in your region play close to 100% traditional music, mainly from Argentina and Uruguay, from the 1920s up to about the early 1960s, mostly by a short list of well-liked orquestas. If you're in a community where modern tango, neo-tango, tango electrónico, alternative music, etc. is prevalent, it might be bad advice.)