Here's my take: What she is communicating to you is not "it's not a hobby". What she's trying to communicate (and has, it sounds like) is "I don't want you spending money on a new CD player and amp". After hearing this, you justified the purchase by saying it's a hobby, so now she counters with "technically, it's not a hobby".
Your secondary argument over the hobby-ness of audio is not the real issue. You're arguing over money, plain and simple. You're in good company, it's the number one subject of argument among couples. It's interesting that your better half sounded quite accepting of your non-hobby until the purchases crossed her comfort level.
It's not relevant whether audio qualifies as a hobby or not, there's no "true" answer to that question. I would stop looking for ways to convince her, as this usually creates the opposite result of what the convincer intends. My advise to you is to sit down with her when you both are in a good mood, and talk about money. Work out for your relationship what the limits are (if any) on purchases and how you individually can make purchasing decisions while still being a part of a couple. The time and effort you spend here will really pay off, as this subject will come up again and again. When she speaks, listen to her perspective and shut up. When she's all done, tell her you understand her perspective. Then tell her your perspective. Then when that's all done start finding solutions together.
You may end up being able to get all the electronics you want AND have a more fulfilling relationship at the same time. It's all about communication.
