Let's talk a little about the Buddhist idea of detachment, or "non-attachment to things of this world". Let's first remember that the earliest Buddhist teachings are not religious at all, but for more of a manual for how to live life such that one has the greatest level of enjoyment. At some point later, Buddhism picked up the idea of reincarnation (most likely from Hinduism, which already existed at the time), such that all sorts of teachings arose related to how to guide one's self into reincarnation as a better creature/person and eventually reach nirvana, etc. Originally, it looks as if Buddhism was teaching how to reach a good state of living (nirvana) in this life, not the next. Buddhism seems to have started as something closer to "Secular Humanism" along with guidelines as to how to avoid unhappiness in one's daily life. Practices such as meditation were primarily to teach the ability to focus on what's important and avoid getting sidetracked by things which don't matter in the end.
As part of this focus on important matters and avoiding sinking into sadness and depression, the teaching of "non-attachment" arose. Some people interpret "non-attachment" as something more like, "don't get attached to things of this world because that leds to unhappiness ultimately". This is absolutely wrong. Yes, not being attached to anything in their world would avoid unhappiness related to that thing/person/animal ulitmately going away/dying, however such a practice would also lead to not experiencing what happiness this world has to offer! Sure, you can live outside of the world, but there is much happiness to be had in this world as well!
How do we solve this problem of experiencing the happiness of this world while lessening the unhappiness which will ultimately happen? Well... Let's use my own situation as an example. My wife has quite a few auto-immune diseases, including adult onset diabetes and allergies to various foods. She seems to be slowly getting worse and ultimately it could put her into the hospital and kill her. If I wanted to avoid the ultimately unhappiness of not having her around, I could leave now, try to forget her, try to find someone else, etc., but that would leave me without all of the happiness which I currently have by having her around! What to do?
What to do, is to enjoy the happiness of the present while living in the present, and then learn to "let go" when it's time to do so! As a simple example, we can all enjoying a great meal while it's happening but we don't say,"I have to keep eating it! I don't want to stop, ever!" (Ok, some of us may, but that's a different issue!) You enjoy the happiness which life brings while it's happening. You enjoy it as fully as possible, by making use of the focusing skills you learned through meditation, paying attention to things which are in the moment and which matter. Then, when the moment is gone, you celebrate the memory of the events, because remembering is also a way to enjoy and and gain a different type of happiness, from the memory. However, once it's done, once the person is gone, and once you have celebrated and appreciated their memory, it's time to move on.
"Non-attachment" is not about avoiding attachment to things of this world. It's about learning how to let events, people, pets, etc., pass out of your life and not continuing attachment to things/people who are not there. Avoiding life is not the lessson of "non-attachment. Learning to "let go" is the lesson of "non-attachment". As the famous song says, "Let it go!", and look forward to the next thing in an ever-changing life!