I think this is it exactly. But let’s be rigorous:
“I am trying to get you to get a doctorate by holding back marriage.” Still works.
No goal (that I can see), therefore nothing.
No goal (that I can see), therefore nothing.
No goal, therefore nothing (assuming I interpret 5 to mean that 4 is NOT with intent).
“I am teasing you to get you to have sex with me.” This probably will not work, but partly because it interrupts the flirting rather than because she knows that the flirting is going on. Depends on how severe the teasing is, really.
“I am teasing you to get you to have sex with me.” This probably will not work either, same reason as 5.
Assuming no ulterior motives, “I am trying to get you to become a teacher by this encouragement” Still works.
“I am trying to get you to become a lawyer by this encouragement” Okay, here’s an error; it’s clearly not that I can tell you what I’m doing that’s necessary. Or at least, not alone.
So, with the corrections suggested by doing this, the distinction should be:
If the target having full knowledge of what you’re doing doesn’t affect whether it works, it’s influence. If the target having full knowledge of what you’re doing does affect whether it works, it’s manipulation.
Or, to get at why one is immoral and the other isn’t, if there’s deception involved it’s manipulation. If there isn’t it’s influence.
And even ignoring that, “English was like this” is no reason for it to continue to be like that if the alternative is perfectly understandable. Languages change all the time for all kinds of reasons; we don’t use the complex system of verb tenses from Old English, or hither, thither and wither, or yon and yonder, (etc.), so why should we feel obligated to use its pronouns? (side note: which were not the same as modern English pronouns; “you” used to be a second person plural object only, it was thee and thou singular and ye and you plural.)
But yes, “man” used to be gender neutral, and for most of the history of English “they” was the gender neutral third person singular.