Here's why. The rule rests on a profound misunderstanding of how English grammar works. The question is how to analyse the structure of an example like "Our mission is to boldly go where nobody went before". What (exactly) is the "to" doing in "to boldly go"? To take a simpler example, how do "to" and "go" fit together in "I want to go home"?
The anti-split rule is based on the answer given by prescriptive grammarians in the Bad Old Days. (When were the old days bad in grammar? Roughly from 1750 to 1950, give or take a few decades.) They knew a great deal more about the grammar of Latin than about English, so they tried to squeeze English into the mould of Latin.
If you translate "I want to go home" into Latin, the English "to go" translates into a single Latin word ire, called the infinitive. Therefore "to go" is the infinitive of go. So the argument goes that it must really be a single word (in spite of the spelling). In other words, just as going contains a suffix, "-ing", which marks it as a present participle, to go actually has a prefix "to" which marks it as an infinitive.
And splitting? Well, you cannot split going, can you? For example, you cannot push an adverb such as "boldly" between the root and the suffix, to give "We are go-boldly-ing home". So it stands to reason that the same holds true for the infinitive. QED.
This now strikes us as blindingly stupid. The fact is that nobody would dream of splitting "going", whereas everybody is liable to occasionally, and perhaps even frequently and ostentatiously, split "to go".
Back to the drawing board. How do "to" and "go" fit together? Modern grammarians see this as a question for research - we cannot just go and look up the answer in a book.
Different researchers will give you different answers, but a convincing one is that "to" and "go" fit together exactly as, for example, "may" and "go" fit together in "he may go'. So "to" is a separate word, just as "may" is, and just like "may", it can be separated from "go": "he may really crack it", or "I want to really crack it".
A lot of what some people think of as grammar is this kind of prescriptive nonsense from the bad old days.
Fortunately, you will not find anything about split infinitives in the national curriculum, so perhaps (with luck) the next generation will be oblivious to the split-infinitive ban.
Instead, they can concentrate on getting to really know about language in use.
Richard Hudson is professor of linguistics at University College,London.
Geoff Barton is headteacher of King Edward VI School, Bury St Edmunds, Suffolk