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It does not matter at all which word I use for a certain age if I explain what is meant.
But you didn't explain what you meant initially. It was only after you had confused multiple people that you clarified what you meant.
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And with many teenagers and the few years after teen-age, up to late 20s or early 30s or whatever I have certainly no problem to call them "young".
The phrase "young adult" has an established meaning in common usage. You can't just disregard it because you don't like it and expect people not to comment.
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A 30 year old is for sure no old adult. Do you want to call it "mid-adult"?
That sounds stupid. "Twentysomething" or "thirtysomething" is fine.