This is my understanding of why (I'm a learner so I welcome any corrections)
bh often sounds like either /v/ or /w/
BH broad = /w/ BH slender = /v/
When to use broad or slender sound?
Irish vowels are defined as either broad (aáoóuú) or slender (eéií)
The pronunciation of each consonant is determined by the adjacent vowel
Using leabhar as an example:
So, in this case: L + e = Slender L sound
a + BH + a = Broad BH sound (/w/)
a + R = Broad R sound
This is really helpful, if correct.
The way you wrote it all out reminds me of a math problem. If x = y, and z = t, solve for w if wxz = 3ty. (Or something like that! :) )
Although, the first vowel sound still sounds to me more like an "í" (i fada) sound to me, not just a regular "e."
I think this is the same construction as 'Is leamsa ...' ('... is mine') in Scottish Gaelic. "'S ann leamsa a tha ..." would be equivalent to " ... belongs to me", which is subtly different in English, but I'm not sure there's a distinction between the two constructions in Gaelic.
It's my book is more specifically Is é mo leabhar é, but context is important. If you were saying "It's my book, I've been looking for that everywhere", you'd say Is é mo leabhar é, bhí mé á lorg ar fud na háite. On the other hand the answer to "Whose book is this?" - Cé leis an leabhair seo? is Is liomsa an leabhar, which can reasonably interpreted as "the book is mine" or "it's my book", and you could even interpret the question and answer as "Who owns this book?" and "I own the book" ("own" can be a verb in English, but there is no equivalent verb in Irish).
So you're not wrong, but the phrase "it's my book" is ambiguous in English, and can mean two different things.