[susan53]

You need to distinguish between the subject and object of the main clause and the subject and object of the relative clause. In your second example a/the man is the object of the main clause but the subject of the second :
I have found a man (Object). The man (subject) will complete the work
= I have found a man (object) who(subject) will complete the work.
who refers to the object of the previous clause in terms of meaning, but forms the grammatical subject of the relative clause. therefore who is obligatory.

Your first example is different. Here the underlying idea is :
John (subject) is my father. You (Subject) met John (object) yesterday.
So in the relative clause, who replaces the object (John):
John, who(object) you (subject) met yesterday, is my father.

Here, when the relative pronoun replaces the object, whom is grammatically possible but is almost never used except in formal written style. This type of non-defining relative clause is rare in spoken language (as opposed to defining relative clauses - something like Do you remember the man who you met yesterday? John? Well, he's my father) and if you wrote this sentence it would probably be in, maybe, an e-mail to a friend. And so informal, meaning that who would be more appropriate.

When it is used nowadays, it is frequently included after a preposition. So, for example :

... The declining number of school leavers, many of whom enter nursing, will result in an ...
... the larger communities of Turkic-Mongol peoples to whom they were related.
...the party leader, Mr Rezsoe Nyers, with whom he has been waging a long-running feud,
...the fashionable decorator Francis Lenygon, by whom Margaret was casually employed