And it was a very long post, but it must be to attempt to explain away such plain statements. Your argument does not justify men having religious titles such as "father" because of the following:
First, The context of Matt 23 is speaking of the pride of the religious leaders of that day. Jesus is showing such titles used in a religious sense are prideful and forbids it.
Of course he is not condemning the use of the word used in the secular sense, as we are told to "honor mother and father".
This is not a hyperbole because he is showing exactly what the religious leaders were being called by, plainly warning us not to do so.
The word "rabbi" is not used anywhere else in the New Testament except in Matthew 23. Though it is rendered "master" or "rabbi" in other places, it is not the same word your are describing in Matthew 23.
The word you are speaking of is kathēgētēs, and the context Jesus spoke this word, it is used as a religious title.
When we find the word "rabbi" meaning "teacher" in other places like in the Book John is rendered from a different Greek word, for example:
Joh 1:38 Then Jesus turned, and saw them following, and saith unto them, What seek ye? They said unto him, Rabbi, (which is to say, being interpreted, Master,) where dwellest thou?
The word used in this place and every other besides Matt 23 is "didaskalos"
This is not used as a title. It may be a description of what the person does as a teacher, but it would be wrong for me to say, "i now would like to be known as Teacher or Master" because that would be a religious title.
Heb 5:12 says "for when the time comes that ye ought to be teachers...."
This is not the word found in Matt 23, he not saying, "when the time comes that ye should be known as Teacher" but that teaching is what they should have been doing but they were immature.
For men to call themselves "Father" in a religious sense, making it their name and title is doing exactly what Christ forbids.
We are not to call any man "Father" in that sense.
"Our father Abraham" is another sense to show descent, he was not known as "Father Abraham".
Clearly it is a sin for any to take on such a title.