I think you wanted to go for the word appreciate in the sentence. Maybe I should appreciate my own life instead of wishing for someone else's. Wishing for someone else's, in this case, means you want the other person's life. You want what they have going for themselves.

You wish someone else’s life was your life

In the sentence: "Maybe I should be appropriating my own life instead of wishing for someone else's." The phrase "wishing for someone else's" means desiring or wanting to have the life or experiences that belong to another person. It doesn't necessarily refer to property or tangible items but rather to someone else's life, circumstances, or qualities. For example: If someone has an exciting career or a happy family life, and you envy that and wish it were yours, you are "wishing for someone else's life." In this context, the sentence suggests the speaker is reflecting on focusing on their own life rather than envying or longing for what someone else has.

"I should" needs to be followed by an infinitive: "I should appropriate". After changing "appropriating" to "appropriate", the sentence becomes grammatical. However, I think "appropriate" is a poor word choice. You can appropriate someone else's life but it is impossible to appropriate your own. It just doesn't make sense. A better choice would be "take responsibility for": "Maybe I should take responsibility for my own life instead of wishing I were someone else." A simpler, more conversational alternative is: "Maybe I should own my life instead of wishing I were another."

It's flawed from the get-go. First off, it sounds better, at least in a native Westcoast NA accent, as: "Maybe I should experience my own life instead of wishing for someone else's" Secondly, it's talking about wanting someone else's life (as in the lifestyle that they live). Being that life is a combination of self effort and simply luck, I would advise following a Daoist style path of going with the flow of how things are, at least, if you're aiming to live a life of peace and contentment. At least, it seems to have been working pretty well for me! ✌️😁