Is it wrong to split an infinitive?

No, and sometimes splitting it is the only way to say what you mean. To boldly go is not an error.

An infinitive in English is two words — to go, to write — and splitting it means putting an adverb between them: to quickly write. The supposed rule against this comes from the same nineteenth-century impulse to model English on Latin. In Latin an infinitive is a single word, so it physically cannot be split. English infinitives are two words and have been split by good writers for centuries.

The reason it is worth defending is that moving the adverb changes the meaning. Consider:

She failed to completely understand. — she understood, but partially. She failed completely to understand. — ambiguous, and probably means her failure was complete. She failed to understand completely. — again ambiguous.

Only the split version says the intended thing unmistakably. Refusing to split forces either ambiguity or an awkward rewrite.

Where splitting does hurt is when the inserted material is long. To quickly and without any further consultation approve strains the reader, because the two halves of the infinitive end up too far apart to connect. A short adverb is fine; a clause is not.

All the major style guides now accept split infinitives, several explicitly recommending them where they improve clarity.

If you are writing for someone who believes the rule — some editors and examiners still do — the safe move is to place the adverb where it reads best and be able to explain the choice, rather than mangling the sentence pre-emptively.