Inf     initives
Infinitives in the Romance languages can't be split because the particle signifying that the verb is an infinitive is attached to the base word itself. In French, the "er" in "parler" is equivalent to the "to" of English's "to talk." So in the Romance languages, it's impossible to split an infinitive. But the grammarians of yore decided that English, though not a Romance language, must follow that model even though its infinitives were already split and just waiting for an adverb to be slid between the two parts.

Imagine that America decided to modify one of its football rules so that it accorded with that of British football. For example: Henceforth, no player of American football shall touch the ball with his hands. So you wind up with all these padded guys running around trying to play the game in its usual fashion with that one useless exception. To fashion (or refashion) the rules of one game according to the rules of a fundamentally different game puts unnecessary limits on the changed game and really makes very little sense.

I don't think we should go around splitting infinitives for the heck of it, but I think we should leave the option open. Sometimes, it's more awkward to put an adverb before or after the infinitive than it is to plop it right in the middle.

A similar phenomenon that doesn't receive as much attention is the placement of adverbs between helping verbs and main verbs. Most of us prefer "he has often been seen walking" to "he often has been seen walking" or "he has been seen often walking." The original placement of the adverb eliminates ambiguity. There is no doubt that "often" modifies the frequency of his having been seen rather than the frequency of his walking. The placement also eliminates awkwardness of speech -- it sounds very artificial in many cases to place the adverb before its accompanying verb.

The splitting of main and helping verbs is congruent with the splitting of an infinitive; it's a separation of verb parts by an adverb. Yet teachers of English don't squawk half as much when it's not an infinitive being split. Teachers are taught to have this pet peeve without knowing why they have it and without considering similar cases that don't disturb them. And they pass their ignorance along to further pupils. All we need is to better educate our educators.