A hobby is an inseparable part of one's self-development. Hobbies are an inseparable part of everybody's [or one's] self - development. Both are fine and basically mean the same thing.

Tom is right, though. You could use either sentence even in the context you mentioned. Its about verb/subject agreement - "a hobby is". or "Hobbies are."

Maybe an “an essential part of self development”

thank you, Tom! The point is that earlier in the essay lots of hobbies have been discussed, so the Conclusion is about the role of hobbies, many hobbies. Thanks again!