Naomi’s answer is good. Let me add a bit more. Your version 2 assumes that the missing/implied word after “belonging to” is “yourself”. I can see why you thought that. But, the missing/implied word is in fact “something”. It’s “something” that you must both “belong to” and “serve.” And the final piece is that this “something” is “beyond yourself”, or “other than yourself.”

In the first sentence, the word "belonging to" implies belonging to a family, community or something other than YOURSELF. This is especially so because of the ending of the sentence. It says "serving something beyond yourself". In other words, serving something other than yourself, something in addition to yourself. A very nice thought! In the second sentence, saying "serving YOURSELF" means putting yourself first, before others. Therefore, it means the opposite. The second sentence does make sense because it suggests two different ideas. It would be more in harmony to say, " Meaning comes from belonging to YOURSELF and doing your own thing". A selfish thought. Hope this helps