Like the word February, there is a tendency for some speakers to leave out the r sound after the b in library, resulting in libary as the pronunciation. The r is not silent, though, so the standard pronunciation calls for leaving the br sound in place.
library
Posted in Pronunciation.
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Personally, I feel that this pronunciation is none other than lazy. It shows a lack of effort.
It has nothing to do with laziness for most. We learn to say words before we learn to spell them. We pick up the pronunciation we are exposed to, and tend to stick with that pronunciation, even when—as with so many words in the English language—the spelling appears not to be phonetic.