To prove that Paul was not teaching or telling other people to forsake Torah, they devised a plan to show that he would participate and complete a Nazarite vow. Thus proving he was not walking contrary to Torah, and telling people otherwise.
I can appreciate that you can see this particular text the way that you see it, but the bigger picture shows that Paul believes the Law of Moses has been set aside.
Before I offer an explanation of how this account from Acts can be coherently explained in terms of a view where Paul believes the Law is coming to an end, let me remind all of the formidable Biblical evidence that the Law of Moses is retired:
1. Ephesians 2:15 - a direct declaration of the abolition of the Law of Moses;
2. That text in Galations where Paul likens the Law to a tutor whose job comes to an end when the child being tutored grows up;
3. A statement in Romans 10 about Christ being the end of the Law;
4. A statement in Colossions about how "the Law" is nailed to the cross;
5. Peter's vision of the animals in Acts - God tells Peter that all foods are now clean (in contradiction to the Law of Moses);
6. Jesus' declaration that all foods are clean (e.g. Mark 7);
7. Jesus acting as though as though He, and not the temple as the Law requires, is the place to go for forgiveness,
8. Jesus boldly declaring that He is the new Temple ("Destroy this Temple and it will be rebuilt in 3 days"). Let's not forget, the Law of Moses requires the Jew to go the Temple for purification;
9. The tearing in two of the curtain in the Temple - how can one say the Law of Moses lives on when a central element needed for carrying it out - the temple veil, has been torn in half;
10. Jesus intentionally becomes unclean, according to the Law, by touching a woman with a menstrual bleed.
....and that's just a start.
Now the Acts 21 passage: Yes, Paul
follows the law in this instance,
as does Jesus in some cases. But, I suggest that both men are doing this even though they believe the time of the Law of Moses is coming to an end:
Jesus obeys the Law to delay His arrest till the appropriate time.
Paul obeys the Law here in the interest of appeasing his fellow Jews - he is no dummy; he knows that he needs to "pick his battles".
I think that Dr. Robert Thiel handled this question better than I could...
What Was Nailed to the Cross?
Since all scripture is given by the inspiration of God so that Christians should be complete (2 Timothy 3:16-17), it is wise to look at more than one verse to determine what, for example, was nailed to the cross.
There is only one only scripture that uses the "nailed it to the cross" expression (AV/NKJ), it is Colossians 2:13-14, in which Paul states,
"And you, being dead in your trespasses and the uncircumcision of your flesh, He has made alive together with Him, having forgiven you all trespasses, having wiped out the handwriting of requirements that was against us, which was contrary to us. And He has taken it out of the way, having nailed it to the cross".
We will look at what it does and does not say.
First though, let's look at what the last chapter of the last book of the Bible teaches:
"Blessed are those who do His commandments, that they may have the right to the tree of life, and may enter through the gates into the city" (Revelation 22:14, NKJV throughout unless otherwise noted).
Since it is only "those who do His commandments...{who} have the right to enter...the city" (Revelation 22:14), the ten commandments could not be "contrary to us". Actually, it is only those who will not keep the ten commandments that are denied access. Revelation specifically shows that those who break one of at least four of the ten commandments will be outside God's city (Revelation 22:15).
So then, if the ten commandments were not "nailed to the cross," what was?
Look again at what the Bible actually says (two translations):
14 having wiped out the handwriting of requirements that was against us, which was contrary to us. And He has taken it out of the way, having nailed it to the cross (Colossians 2:14, NKJV)
14 having canceled out the certificate of debt consisting of decrees against us, which was hostile to us; and He has taken it out of the way, having nailed it to the cross.. (Colossians 2:14, NASB)
The handwriting of requirements (often also called the hand-writing of ordinances) or certificate of debt was wiped away and nailed to the cross.
Which requirements were wiped out?
Please understand that the expression "the handwriting of requirements" (cheirógrafon toÃs dógmasin) is a Greek legal expression that signifies the penalty which a lawbreaker had to pay--it does not signify the laws that are to be obeyed--only the penalty. It is only through the acceptance of the sacrifice of Jesus Christ that the penalty was wiped out ("the handwriting of requirements"). But only the penalty, not the law!
Even some Protestant commentators realize this is so. Notice what Matthew Henry's Commentary on the Whole Bible states about Colossians 2:14:
Whatever was in force against us is taken out of the way. He has obtained for us a legal discharge from the hand-writing of ordinances, which was against us (v. 14), which may be understood,
1. Of that obligation to punishment in which consists the guilt of sin. The curse of the law is the hand-writing against us, like the hand-writing on Belshazzar's wall. Cursed is every one who continues not in every thing. This was a hand-writing which was against us, and contrary to us; for it threatened our eternal ruin. This was removed when he redeemed us from the curse of the law, being made a curse for us, Gal 3:13. (from Matthew Henry's Commentary on the Whole Bible: New Modern Edition, Electronic Database. Copyright (c) 1991 by Hendrickson Publishers, Inc.).
In addition, let us look at the Greek term exaleipho translated as "wiped out" in Colossians 2:14:
NT:1813
exaleipho (ex-al-i'-fo); from NT:1537 and NT:218; to smear out, i.e. obliterate (erase tears, figuratively, pardon sin) (Biblesoft's New Exhaustive Strong's Numbers and Concordance with Expanded Greek-Hebrew Dictionary. Copyright (c) 1994, Biblesoft and International Bible Translators, Inc.)
In other words, exaleipho has to do with wiping out sin. This is also confirmed in Acts 3:19 where Peter also uses the term exaleipho, which is translated as "blotted out" below:
19 Repent therefore and be converted, that your sins may be blotted out, so that times of refreshing may come from the presence of the Lord.
Hence, it is sin and the related penalties that are to be blotted or wiped out. And the penalties could vary from "being unclean to the evening" (Leviticus 11:24-28) to making an offering (Leviticus 5:5-6) to being "cut off from his people" (Leviticus 7:27) to the death penalty (Exodus 31:14).
This is also confirmed elsewhere in the New Testament:
13 Christ has redeemed us from the curse of the law, having become a curse for us (Galatians 3:13).
The curse of the law is related to the penalty. And Jesus paid it.
But what about the law of God? Was the law of God to be wiped out?
Remember that the Bible clearly teaches that sin is lawlessness:
Whoever commits sin also commits lawlessness, and sin is lawlessness. And you know that He was manifested to take away our sins, and in Him there is no sin. (I John 3:4-5).
Notice that Paul wrote:
Shall we continue in sin that grace may abound? Certainly not! How shall we who died to sin live any longer in it? (Romans 6:1-2).
Thus the New Testament makes clear that the law of God continues, thus it was not nailed to the cross or somehow wiped out.
The Bible, however, also shows that the requirements of the Levitical priesthood (Hebrews 9:1,6-10) sometimes called the law, which were part of the penalty of sin, were blotted out.
And why?
"For it is not possible that the blood of bulls and goats could take away sins...By that will we have been sanctified through the offering of the body of Jesus once for all" (Hebrews 10:4,10).
Jesus' one sacrifice was and is sufficient--we do not have to sacrifice animals any more!
Another requirement (which is related) would be the death penalty of sin, as "the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord" (Romans 6:23) or other specific ceremonial penalties associated with the Old Testament statutes (such as making a sin offering, being put outside the camp, or washing).
For those who wish to look them up, perhaps most of the statutes in the Old Testament are listed in the following chapters: Exodus 20-24; Leviticus 16-27; Numbers 18-19, 27-30, 35-36; and Deuteronomy 12-18.