I think the sense of confusion is partly coming from the terminology. I know they use the word attachment a lot in Buddhist literature, but maybe its just the best translation and they have a better word in Sanskrit or Tibetan or whatever. Attachment in English has a lot of baggage, especially coming from the field of psychology. It's hard for us to conceive how we can love someone without being attached to them IYKWIM.
Sometimes it helps me to think in terms of the other words they sometimes use like 'clinging' and 'grasping'. They give more of a sense of trying to hold on to what is without all the excess baggage that goes with the word attachment. When you think in terms of clinging/grasping it is much easier to see how you can love without these elements, but also how easy it is for those feelings to sneak in. Loving without clinging or grasping to me means appreciating the moment but allowing it to pass without trying to hold on to it. Still tricky ... but maybe not impossible.
Does that help at all?