Many have a warped view on detachment. It is not about setting aside your care; it's about recognizing three things: you are a vessel for your emotions, you are not in control, and the importance of discernment. I'm making this post because I want to help people obtain the peacefulness that comes from detaching with care.
First, you must understand that your conscious mind, "I," is separate from your thoughts, dreams, and emotions, which are your unconscious mind. Many creative people, such as Michael Jackson, William Blake, and Elizabeth Gilbert, have said that ideas come to them, insinuating that they do not "come up" with ideas themselves. Think of yourself as a vessel. Your unconscious mind is constantly taking in your experiences/memories, and from it, images, thoughts, and emotions arise. Then, your conscious mind, "I," becomes aware of what has surfaced.
You did not consciously choose to feel the emotions you feel; they simply appear. Now, how you (the conscious mind) choose to react is all you can control. But how are you meant to control the emotions that are surfacing in the conscious mind? You allow them to exist; you remind yourself that you are not your emotions and that they will pass. Which leads me to my next point.
Admitting no control actually makes you in control. If you give everything to what you do, then you have no reason to punish yourself for an outcome that is out of your control. You can only be the best you that you can be, and then what happens, happens. So, you should come at situations with the confidence that you will be okay if something falls apart. Any negative thoughts about yourself are not real, but your brain does not know the difference; you must remind it.
Now, because the brain is so gullible, you can actually use that to your advantage. This is when having no control gives you all the control because the truth is, there's no such thing as "no control." You control the ability to pay attention to your unconscious mind and take action. Imagine if Shakespeare never wrote down an idea because he let himself believe that he didn't have the talent for it. Unfortunately, it happens every day because people allow negative thoughts to become their reality. If a genius idea doesn't become reality until its vessel does something about it, then can't the same be said about self-doubt?
Instead of letting a negative thought control you, let discernment distinguish whether or not it's true. You can feel fear, sadness, and anger without letting it decide what you do. You use discernment every day, when you decide to not cross the road after seeing that cars are coming or when you throw out expired food because it could hurt you, even if you really want to eat it. That is discernment, the ability to understand what you are feeling or doing and determine what to do next.
Discernment is so important because empathy without it is no longer empathy; it's self-punishment. It's also not about ignoring the feeling; it's about understanding it. Sometimes the feeling is trying to tell you something, and other times it is just something you need to move forward from. The more you apply discernment in your life, the easier it becomes to tell the difference. You can care about something deeply without letting your emotions make a decision for you. That is what detachment with care is about: feeling your emotions but not allowing them to punish you.