Whoever therefore shall confess me before men, him will I confess also before my Father who is in heaven. Mat 10:32 Our confession of Jesus Christ as Saviour and Lord is critical for the New Birth.

This verse is talking about public confession.   It is not talking about confessing your faith in private to a select few people.   

But whoever shall deny me before men, him will I also deny before my Father who is in heaven. Mat 10:33 Jesus is saying that to willfully and verbally deny Him before men is the Unpardonable Sin.     Why is believing on Jesus and confessing Him before men so important?      Because Jesus is 'God'.     No one can be accepted by 'God' who has rejected Him.      He states that a person's words against Him requires Him to speak against them to the Father.      What does that mean?      It means that His Holy Spirit will not dispense Grace to the denier and leave them to inevitable destruction.      If Jesus is not a person's advocate before His Holy Spirit they are condemned to the Lake Of Fire Mat 12:32.      Faithfulness is a characteristic of the Lord.     If faithfulness is not a part of a person's character they will deny Him eventually.     A person's denial of Him will require His denial of them.

To deny Christ is to not confess Him publicly.   

So where did the notion of keeping one's faith private come from?   
You guessed it.   Satan

If he can't keep a person from believing in Christ, he does the next best thing: He keeps them from confessing Christ Jesus as personal Savious and Lord.   

The best thing a new believer can do is to tell everyone in their life that they have accepted Jesus as Saviour.   

"But what if some of my friends or family are not believers.   Won't they be offended and turn away from me?"

Some might.   But most will likely be drawn to the excitement that you are experiencing and become believers based on your testimony.   

And that us exactly what Satan does not want to happen.   

So, he came up with the 'keep your faith personal and private' scam which
   → effectively gets you to deny Jesus
   → keeps others in your circle from coming to Christ

You cannot offend someone by testifying of Christ Jesus.   If they are offended by your testimony they are actually offended by Christ Jesus, Himself.   

And a stone of stumbling, and a rock of offence, even to them which stumble at the word, being disobedient: whereunto also they were appointed. 1Pe 2:8 Those who reject Christ remain lost in bondage to the Sin Nature, in darkness unable to distinguish good from evil.     They are disoriented and incapable of finding there way out.