Inappropriate means "not appropriate". "Appropriate" means "suitable or proper". Therefore, inappropriate means "not suitable" or "not proper," or "unsuitable/improper".
Unfortunately, what is "appropriate" has usually been a judgment call, one which is based solely on the moral beliefs held by the speaker.
Normal vs. normative
This is similar to the problems with the word "normal". What is abnormal is that which is not "normal," while that which is "normal" is that which is not abnormal.
There exists another word, "normative," which relies on empirical data for its definition. A standard is first established, through properly done research, research which applies the scientific method: this may be applied to human behavior by establishing a baseline of behavior(s) which is agreed upon as the "standard," and then bracketing that behavior with one or more "standard deviations".
Childhood (meaning the time of life for young people who are below 6 or 7 years old) sex play has finally been established to be normative behavior. Research did not begin on the question of childhood sexuality until about the mid-twentieth century: from the mid- to late 18th century, the accepted wisdom (theorized only, and not based on empirical research) held that children were asexual; that is, that children lacked any interest in sex, had no sex drive, and did not "normally" engage in sexual activity. An exception to this was masturbation--masturbation was indeed seen as common, and very destructive behavior in children as well as adults. Children who masturbated often had their genitals mutilated in an effort to prevent the children from continuing to masturbate.
Both these "theories" have now been demonstrated to be totally false: masturbation causes no harm, and children do have an interest in sex, children do have (at least a form of) sex drive, and children do engage in sexual activity, either alone, with peers, with older children/teenagers, and sometimes with adults.
If those who use the word "appropriate" mean "normative," when speaking of sexual activity engaged in by children, then this behavior is appropriate. If those who use the word "appropriate" are making a moral judgement, then that is all that it is--an expression of disgust felt by the speaker regarding behavior which is actually "normative".
(more to be added) Inappropriate child sexual activity
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