How come an apostle contradicts Jesus’ teaching?

I have read, more than twice, that Paul calls Jesus´ disciples “my son”. Were these people his true sons or he was using the rabinical formulae: Rabbi? (Matt 23:8-10).

Paul often used these “banished” words that I don´t see any other Jesus´disciple (or apostle) might have used for others who trusted Jesus as Savior:

1Co 4:17  “For this cause have I sent unto you Timotheus, who is my beloved son, and faithful in the Lord, who shall bring you into remembrance of my ways which be in Christ, as I teach everywhere in every church.”

( 1Co 4:17  That is why I am sending Timothy to you. He is my son in the Lord. I love him and trust him. He will help you remember the way I live in Christ Jesus--a way of life that I teach in every meeting of the church wherever I am. )

Phm 1:10  “I beseech thee for my son Onesimus, whom I have begotten in my bonds…”

( Phm 1:10  My request is for my child Onesimus, the child of my chains, ).

2Ti 2:1  Thou therefore, my son, be strong in the grace that is in Christ Jesus.

 ( 2Ti 2:1  Timothy, my child, Christ Jesus is kind, and you must let him make you strong. )

1Co 4:15  For though ye have ten thousand instructors in Christ, yet have ye not many fathers: for in Christ Jesus I have begotten you through the gospel.

1Co 4:14  I write not these things to shame you, but to admonish you as my beloved children.

Gal 4:19  My little children, of whom I am again in travail until Christ be formed in you (…)

Maybe I´m wrong, but I wouldn´t like to address any this way (even to my own children):

1Ti 1:2  unto Timothy, my true child in faith: Grace, mercy, peace, from God the Father and Christ Jesus our Lord.

Tit 1:4  to Titus, my true child after a common faith: Grace and peace from God the Father and Christ Jesus our Saviour.

Rom 4:16  For this cause it is of faith, that it may be according to grace; to the end that the promise may be sure to all the seed; not to that only which is of the law, but to that also which is of the faith of Abraham, who is the father of us all.

 This is a loving connection:

Php 2:20  With the blessing of the Lord Jesus, I hope I will be able to send Timothy to you soon. I will be glad to learn how you are.

Php 2:20  I have no one else like Timothy, who genuinely cares for you.

Php 2:21  Others are interested only in their own lives. They don't care about the work of Christ Jesus.

Php 2:22  You know the kind of person Timothy is. He has served with me in telling the Good News like a son with his father.

Many  young people –today- are using the same wording Paul used -not being OLD men or women! (but they usually introduce them as “sons” or “daughters”). Are they their real father or mother? That´s paulinism!

I will not dismiss Jesus´s teaching on this subject:

Mat 23:8  "But you must not be called 'Teacher.' You are all equal as brothers and sisters. You have only one Teacher. (Is this another fault we commit at Bible schools?)

Peter has also said, infrequently: “my son”:

1Pe_5:13  The church that is at Babylon, elected together with you, saluteth you; and so doth Marcus my son.

(  1Pe_5:13  The church in Babylon sends you greetings. They were chosen just as you were. Mark, my son in Christ, also sends his greetings.  )

But, in the case of John, was he too old or missing not having (or having had) a family?

I don´t know, but he has said “my children”; but not in patristic way of Paul´s fashion:

1Jn_2:1  My little children, these things write I unto you, that ye sin not. And if any man sin, we have an advocate with the Father, Jesus Christ the righteous:

1Jn_3:18  My little children, let us not love in word, neither in tongue; but in deed and in truth.

3Jn_1:4  I have no greater joy than to hear that my children walk in truth.

For me it´s clear that traditions prevail over certain teachings, even belonging to God or His Christ. We may say this wording came by loving affection, with very much cherished people, but the spirit, the attitude is what makes clear the feeling of men´s heart. These things, together with human wrong doings, are the facts that disappoint unreached (men and women) to avoid those who are converted to a religion and not to a living God.