
Lois P. answered 06/25/19
English Expertise - 3 Years of ESL and Tutoring
Yes, I believe the phrase "my friend" can be misleading with the implication that the speaker has only one friend, that is unless there was a prior discussion about a specific friend. Then saying "my friend" is indicating the friend they were just talking about and that is correct.
However, the use of "a friend of mine" does vaguely point to the fact that the speaker is indicating one of his several friends without being specific. This is more acceptable.
If one were talking about family members it is not common that the speaker would have many brothers, but even if he did, saying "one of my brothers" is highly uncommon. It's usually just "my brother" or "my sister". An instance where I could see the former phrase being used would be back when families were larger and the speaker said something like "an uncle of mine fought in World War II." Or perhaps "a cousin of mine had that same disease", being we all usually have many cousins. The context is very important.