He explains how English is one of two languages where you CAN split an infinitive and why we say say 'I am reading a book.' when nearly everyone else says 'I read a book.'
There is a similar section in the book I read. They used the example, ‘I paint.’, ‘I am painting.’ and ‘I am a painter.’ and how difficult it is to easily convey in another language the same information that a native English speaker would automatically infer by reading the sentences.
I paint = I paint (for enjoyment, not as a profession).
I am painting = I am (at this moment in the act of) painting.
I am a painter = My profession is painting.
