This structure using "tener + past participle" doesn't have an "exact" translation in English. What you're suggesting with "I have read half the book" would really be if you want a literal translation: "He leído medio libro/la mitad del libro", using haber as the auxiliary verb.
This is precisely what we want to highlight here in this lesson, that using tener would give that extra nuance of accumulation that "haber" doesn't have.
That results in different ways to translate in English. We used the most natural translation in English: I'm halfway through the book - where you get that nuance of having got to that point, showing "accumulation".
I hope this clarifies it.
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