"On the contrary" - for the word contrary refers to things that are not the same; that differ from and or with one another; and that are even opposed to one another.
Whereas the phrase "visa versa" refers to things that are part of one another.
Contrary...
Acts 17:7 Whom Jason hath received: and these all do contrary to the decrees of Caesar, saying that there is another king, one Jesus.
Acts 18:13 Saying, This fellow persuadeth men to worship God contrary to the law.
Acts 23:3 Then said Paul unto him, God shall smite thee, thou whited wall: for sittest thou to judge me after the law, and commandest me to be smitten contrary to the law?
Acts 26:9 I verily thought with myself, that I ought to do many things contrary to the name of Jesus of Nazareth.
Romans 11:24 For if thou wert cut out of the olive tree which is wild by nature, and wert graffed contrary to nature into a good olive tree: how much more shall these, which be the natural branches, be graffed into their own olive tree?
Romans 16:17 Now I beseech you, brethren, mark them which cause divisions and offences contrary to the doctrine which ye have learned; and avoid them.
2 Corinthians 2:7 So that contrariwise ye ought rather to forgive him, and comfort him, lest perhaps such a one should be swallowed up with overmuch sorrow.
Galatians 5:17 For the flesh lusteth against the Spirit, and the Spirit against the flesh: and these are contrary the one to the other: so that ye cannot do the things that ye would.
Colossians 2:14 Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross;
1 Thessalonians 2:15 Who both killed the Lord Jesus, and their own prophets, and have persecuted us; and they please not God, and are contrary to all men:
1 Timothy 1:10 For whoremongers, for them that defile themselves with mankind, for menstealers, for liars, for perjured persons, and if there be any other thing that is contrary to sound doctrine;
1 Peter 3:9 Not rendering evil for evil, or railing for railing: but contrariwise blessing; knowing that ye are thereunto called, that ye should inherit a blessing.
Galatians 2:1 Then fourteen years after I went up again to Jerusalem with Barnabas, and took Titus with me also. 2:2 And I went up by revelation, and communicated unto them that gospel which I preach among the Gentiles, but privately to them which were of reputation, lest by any means I should run, or had run, in vain. 2:3 But neither Titus, who was with me, being a Greek, was compelled to be circumcised:
At which point he relates why he had had to return up to Jerusalem to communicate unto them that gospel which he preached among the Gentiles...
2:4 And that because of false brethren unawares brought in, who came in privily to spy out our liberty which we have in Christ Jesus, that they might bring us into bondage:
In other words, because some were being "contrary to" what Paul was preaching among the Gentiles. Thus, Paul's opposition.
Galatians 2:5 To whom we gave place by subjection, no, not for an hour; that the truth of the gospel might continue with you.
He then goes on to relate the even further contrast that as a matter of fact...
Galatians 2:6 But of these who seemed to be somewhat, (whatsoever they were, it maketh no matter to me: God accepteth no man's person: ) for they who seemed to be somewhat in conference added nothing to me:
He related to them that he had been given authority to preach the gospel he preached among the Gentiles.
In contrast they added nothing to this assertion of his.
Instead, they simply agreed with this difference.
2:7 But contrariwise, when they saw that the gospel of the uncircumcision was committed unto me, as the gospel of the circumcision was unto Peter; 2:8 (For he that wrought effectually in Peter to the apostleship of the circumcision, the same was mighty in me toward the Gentiles: )
Galatians 2 :9 And when James, Cephas, and John, who seemed to be pillars, perceived the grace that was given unto me, they gave to me and Barnabas the right hands of fellowship; that we should go unto the heathen, and they unto the circumcision.
Why did they agree with him? How did they even know he was of God?
They perceived his Apostleship had been given him by the Lord.
By what means had they been able to perceive that?
"For he that wrought effectually in Peter to the apostleship of the circumcision, the same was mighty in me toward the Gentiles: )"
The words "he that wrough effectually in" and "the same was mighty in me" refer to the fact that just as God had confirmed the Twelve's Apostleship as being of God via the Spirit's miraculous signs, He confirmed the validity of Paul's Apostleship of the Gentiles to James, Cephas, and John in a similar manner.
The Twelve's Apostleship confirmed via signs...
Mark 16:19 So then after the Lord had spoken unto them, he was received up into heaven, and sat on the right hand of God. 16:20 And they went forth, and preached every where, the Lord working with them, and confirming the word with signs following. Amen.
Acts 5:12 And by the hands of the apostles were many signs and wonders wrought among the people; (and they were all with one accord in Solomon's porch.
Likewise, as to Paul's Apostleship of the Gentiles...
Acts 15:12 Then all the multitude kept silence, and gave audience to Barnabas and Paul, declaring what miracles and wonders God had wrought among the Gentiles by them.
Acts 19:11 And God wrought special miracles by the hands of Paul:
Acts 21:19 And when he had saluted them, he declared particularly what things God had wrought among the Gentiles by his ministry.
Galatians 3:5 He therefore that ministereth to you the Spirit, and worketh miracles among you, doeth he it by the works of the law, or by the hearing of faith?
Romans 15:15 Nevertheless, brethren, I have written the more boldly unto you in some sort, as putting you in mind, because of the grace that is given to me of God, 15:16 That I should be the minister of Jesus Christ to the Gentiles, ministering the gospel of God, that the offering up of the Gentiles might be acceptable, being sanctified by the Holy Ghost. 15:17 I have therefore whereof I may glory through Jesus Christ in those things which pertain to God. 15:18 For I will not dare to speak of any of those things which Christ hath not wrought by me, to make the Gentiles obedient, by word and deed, 15:19 Through mighty signs and wonders, by the power of the Spirit of God; so that from Jerusalem, and round about unto Illyricum, I have fully preached the gospel of Christ. 15:20 Yea, so have I strived to preach the gospel, not where Christ was named, lest I should build upon another man's foundation: 15:21 But as it is written, To whom he was not spoken of, they shall see: and they that have not heard shall understand.
