Some months back I noted how discussions of Buddhism by people not familiar with it outside of its pop-culture incarnation often end with them misconstruing it or dismissing it entirely. "Life is suffering" sounds terrible, but the way I put it, a better way to think about the first of Buddhism's four "noble truths" would be "Life and suffering are inextricable". The same goes for the second line item, often described as "The source of suffering is attachment".
Once again, translation is something of our enemy here: "attachment" is commonly used as a translation for the word dukkha, which some folks have made a case for leaving entirely untranslated as a way to get people to fill the word with the meaning it deserves. "Craving", "thirst", "desire", "longing", "need", "unfulfillment" — if you add up enough of those words, you get a composite meaning for dukkha. In the end, all it really is about is wanting this and not that, and getting peeved because the universe's waiter isn't listening when you give it your order. You wanted the eggplant parmesan, not the lentil soup!
But again, a lot of folks dislike the sound of this. They think it means they're being told that to have an opinion, or a desire, is a bad thing. For most people, that's neither realistic nor possible anyway. What it does mean, as I've come to see it, is that you have to see your likes and dislikes for what they are: as manifestations of your particular desires, and not the sum total of your personality.
In other words, it means looking at your emotions and not thinking that they're "you", but just products of an ongoing process. The whole set of mental practices that Buddhism advocates is meant to help someone find that state all the more readily, so they don't spend as much time thrashing around in the swamp of their own ego. It's not meant to teach people how to be ascetics — although you can do that if you're so inclined; it's just not likely to do much more than give you a new way to frustrate yourself.
"It's not the thing that's bad, it's wanting it" is also a slightly misleading if earnest way to talk about this concept. It's not even the wanting of the thing that's bad. (If I didn't want other people to prosper, and didn't work for such a goal, how's that supposed to be good?) It's when you can't see the wanting for what it is — wanting, rather than an inevitability or a concrete reality.
You aren't your thoughts or your desires, and the whole point of practicing this stuff is to make that more than just a nice-sounding idea. It's to make it into a livable ideal.
So, how to rephrase this? If "the source of suffering is attachment" doesn't quite cut it, how about "not recognizing the source of suffering is attachment is the source of suffering"? Convoluted, maybe, but closer to the truth in terms of what you have to do and not just what you have to think about.