The excuse I heard was that
an infinitive in English is two
words but corresponds to a single
word in Latin, and, of course, as
all good Latin experts know, English
grammar should be as much like Latin
as possible! So, since can't split
a single word infinitive in Latin,
we shouldn't in English! So,
"to be" is okay but "to not be" would
be bad. "To an infinitive split" would
be awful! So, string me up if I were
to badly split an infinitive!
Sometimes it just sounds better. Why it does is an interesting question for linguists.
"To boldly go where no man has gone before"
"We are determined to completely and utterly eradicate the disease."
"She wants to gradually get rid of her teddy bears."
"Writers should learn to not split infinitives."
It's also not always possible to eliminate the split infinitive, or the infinitive, without changing the direct or implied meaning of the sentence. "She wants to get rid of her teddy bears gradually" works fairly well.
"Boldly going where no man has gone before" is close, but doesn't capture the same challenge, summons, call to action as the original. Nor does it sound as pleasing.
Problem is, without thinking about
the likely meaning, at first glance
it's not clear what 'gradually' modifies,
that is, it may modify 'wants', that
is, her wanting is only gradual and
not yet full; such are some of the
possibilities of subtlety of meaning
with the English
language!