Greetings in the name of our Lord, Jesus.....peace to you and yours.
I have a research question and having problems finding meaningful analysis:
Acts 15:10 -What was Peter really saying?
Is he agreeing with Paul? What am I missing? Please advise.
Peter in Acts 15:10 says:
 Now therefore why tempt ye God, to put a yoke upon the neck of the disciples, which neither our fathers nor we were able to bear?
You ask was Peter agreeing with Paul. The answer is yes. But what Peter agreed to is only what Jesus taught: exaggerated interpretations of the Law given Moses beyond its express scope places undue burdens on people, both Jews and Gentile. Luke 11:46; Mark 7:6-9. Peter was not agreeing to an entire rejection of the Law (which no one in this passage declares). Peter rejects the exaggerated application of the Law "which neither our fathers nor we were able to bear."
To see this, you start with verse 5 of Acts 15. There were some Pharisees who insisted Gentiles be circumcised if they converted. But that was not a command in the Law applicable to Gentiles. Instead, the circumcision command only applied to the sons of Israel. (Lev. 12:2-3, "speak unto the sons of Israel".) The Law had distinct commands for Israel versus foreigners/sojourners. While foreigners/sojourners (Gentiles by definition) were commanded many things in common in the Law, there were many distictions between the two. Yet, the circumcision was not one of the commands God imposed on Gentiles in the Law.
The same reasoning that exaggerated this circumcision command to Gentiles was the same exaggeration by the Pharisees which taught the Jewish people to wash their hands before eating. The Pharisees portrayed this rule as supposedly a command from God which made you a sinner if you did not do it. Jesus faulted the Pharisees for putting undue burdens on the people such as handwashing which were mere traditions of men. (See Mark 7:6-9.)
Jesus similarly speaks about the religious leaders doing this in Luke 11:46: "You burden people with loads that are hard to carry." This is very reminiscent of what is the issue in Acts 15. James even says "to not make it more difficult" for Gentiles to become disciples. (Acts 15:19.)
Now go back to Acts 15:10. The term "yoke" symobolizes doctrines. Jesus said "take my yoke" and "learn from me." It meant a set of commands/teachings.
Hence, in Acts 15:10 when Peter says "why put a yoke on the neck on [Gentile] disciples," he means why put a set of teachings on yourself. What characterizes these teachings? He says "Neither our father nor we are able to bear."There are only 2 choices what this means.
Either he meant the yoke were teachings that exaggerated commands in the Law beyond what the Law required. This in context fits because verse 5 speaks of the fact the Pharisees exaggerated the circumcision command beyond Israelites. And James in Acts 15:19 speaks of not putting unnecessary burdens on Gentiles.
However, some opt for the other alternative that Peter supposedly meant circumcision was a yoke to Jews, and why would we want to impose on Gentiles circumcision when 'we [Jews] could not bear it.'
However, it is unlikely Peter meant circumcision was a yoke on Jews now cast off. Peter uses the term "yoke" which to repeat here means metaphorically a set of teachings, not a single command. Also, if Peter's remarks were construed to imply God was abrogating circumcision also as to Jews, then two incongruities arise.
First, James was participating in this Acts 15 meeting, but in Acts 21 James tells Paul that the ruling on circumcision in Acts 15 did not mean Jews were freed from compliance with the circumcision duty. Thus, it seems James assumed Peter did not refer to circumcision by reference to the yoke too burdensome for even Jews to bear. Also, if Peter meant circumcision was done away for Jews and Gentiles, we have a supervening injuction from God to regard Peter as an apostate. See Deut. 13:1-5 and Isaiah 8:20. I would make the effort to read Peter in a manner that reasonably avoids that consequence as long as it is textually possible. And that is by reading yoke to mean exaggerated interpretions of the Law in favor of expanding burdens.
In sum, yes, Peter was agreeing with Paul (a) circumcision was not for Gentiles; and (b) in the general principle that exaggerated commands were not something that Jews could bear, and 'why would we want to do the same thing to Gentiles?'
I hope this helped.