BETWEEN SEND-OFF AND SENDFORTH
Send-off is a demonstration of good wishes for a person setting out on a trip, career, or other venture e.g. They gave him a rousing send-off at the pier.
From the grammatical perspective, to send forth means
a.to produce; bear; yield e.g. plants sending forth new leaves.
c.to issue, as a publication e.g. They have sent forth a report to the stockholders.
d.to emit or discharge e.g.The flowers sent forth a sweet odor.
It has become customary for us in Nigeria, and probably some of other non-native English speakers, to arrange "send-forth parties" as an organized expression of goodwill for people who are about to leave us for a new place or for a new venture. This expression, which seems to have originated as a coinage by Nigerian born-again Christians, would certainly make no sense to many Americans and Britons. Its equivalent in standard British and American English is "send-off" (note that it is NOT "send-off party" because "send-off" is a noun, not an adjective) or "farewell celebration" or, rarely, "bon voyage." Americans also call it a "leaving party."
We most times use "send-forth party" because "send-off" seems distant, even hostile. The adverb "forth" appears to us to convey a connotation of forward motion, of advancement, while "off" strikes us as suggesting departure with no expectation of return. So we think that to say we send people off creates the impression that we derive perverse pleasure in their departure from us. But linguists would call this reasoning naïve, if not downright ignorant, because the definition of an idiom—which is what this phrase is— is that it is an expression whose meaning cannot be inferred from the meanings of the individual words that make it up.
The apt word is send-off not "send forth"; not "send-off party".
That is English language for you!