If ever there was a contender for the title of "the mother of a shibboleth" in English, the split infinitive is high up there on the shortlist. Successive generations of gullible pupils were told over and over again by their teachers that split infinitives were unacceptable and an abuse of the English language up with which they would not put, to paraphrase an apocryphal story about Winston Churchill regarding the use of prepositions at the end of a sentence.
As so often before, in his Modern English Usage (1926), H. W. Fowler poignantly pointed out that "The English-speaking world may be divided into (1) those who neither know nor care what a split infinitive is; (2) those who do not know, but care very much; (3) those who know and condemn; (4) those who know and distinguish. Those who neither know nor care are the vast majority, and are happy folk, to be envied."
And R. W. Burchfield, in The New Fowler's Modern English Usage, (3rd edition, revised in 1998)  states "No other grammatical issue has so divided the nation since the split infinitive was declared to be a solecism in the course of the 19th century." Burchfield, in his earlier The English Language (OUP, 1985), had referred to people "suffering from the 'split infinitive' syndrome".
The split infinitive has been part of English literature since around the 13th century although it became rarer in Early Modern English - Shakespeare only uses it once. This would seem to coincide with the fashion for trying to bring English in line with Latin, i.e. it is a "mistaken belief based on a false analogy with Latin" to think that the infinitive cannot be separated.
The argument against the split infinitive is that it breaks the unity of the verb. In the case the verb "to be" is considered to be one unit which cannot be split.
But consider perfect tenses: "I have wanted a dog for a long time" is the same idea as "I have always wanted a dog" but nobody complains about the "always" in the middle.
Although most authorities now agree that such thinking is plain wrong, some writers, possibly mindful of their suffering at school, make an effort to not split an infinitive just in case one of them thar traditionalists, or worse, the odd language pundit, that still abound out there thinks their English ain't up to scratch. Another, possible more plausible, reason is put forward by William Cobbett in his Grammar of the English Language, i.e. such people are "unwilling to treat with simplicity that which, if made somewhat of a mystery, would make them appear more learned than the mass of people".
- "'To boldly go' gets green light"] BBC News
- "Up with which I will not put" (Apocryphal) The Churchill Centre
- "Style guide" The Guardian
- Mayes, Ian. "How to correctly use the English language" The Guardian
- "A case of the split infinitives" David Crystal in English Today
- Johnson. "Gotta split" The Economist
-  Collins Dictionaries
-  World Wide Words
- Split infinitives Oxford Dictionaries
- Hattersley, Roy. "Snobbery and the split infinitive" The Guardian.