I have been a single mother to my son since he was born 14 years ago. His Father lives less than 20 miles from us, but has been in and out of my son's life for years. My son's desire for a relationship with his father peaked at about 11 years old and I began to initiate and facilitate more interactions between them. My son needed to know what kind of man his father is and develop his own opinions about him, both as a father and as a man. Now, at 14, they once again have limited interaction, but that is my son's choice. They simply don't have much in common. It is unfortunate, but his father has reaped what he sowed.
Long way around the bushes for me to say, that as painful as it is, for us, the Mothers, it is important for our sons to know their bio-dads. Early teens are beginning their journey into adulthood and establishing the type of man they will become. They know us, but the Dad, the male half of themselves, they need to come to terms with - to accept what type of man their bio-dad is and to understand that they are different and are not bound by their father's actions.
Your son knows that his father is a flake - unreliable and distant. But he wants to know his 1/2 brother - I think that is commendable. And understandable, as we all have a deep seated desire to know our family.
Take the counselor's suggestion - set up a day trip to, or near, the bio-dad's home. Talk to his wife, if need be, and set up a time and place, a park, restaurant, somewhere, to meet. Let the boys meet. In this day and age, with email and online gaming, etc. if they want to they will be able to keep in touch.
If it fails, and they do not respond, remind your son that when he and his 1/2 brother are both over 18, they can have any contact they desire.
Your son is aware of the reality that is his Dad - he will be hurt if he is not allowed to meet his 1/2 brother - but, don't let yourself be the one who prevents it.
Good Luck and God Bless