Romans 11:16 (ISV)
If the first part of the dough is holy, so is the whole batch. If the root is holy, so are the branches.
What's the connection here?
Is all of Israel holy solely because they are the branches and their root is Abraham/Jesus?
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No, but this passage is more about Gentiles and God's work...
As a hermeneutics site, "how" we arrive at the answer is the most important answer to any question. The first "hermeneutic" here is: context.
In summary, the point is not about whether everyone in Israel is holy, but whether Gentiles who believe Jesus have just as much right to consider themselves as God's children in the New Testament as Israel did in the Old Testament.
In these verses, about 11-24, but also beyond, Paul is talking about how Gentiles are just as equally part of God's redeemed family because of Jesus, just as much as Israel.
He uses the concept of being "grafted" from v17 on, referring to the Gentiles. This is a discussion throughout the entire New Testament and is a theological topic many libraries aren't enough to fill. So, we won't dive into those inexhaustible discussions here.
First and foremost, look at the verses before and after to see that this greater topic of "Gentiles also following God" is what Paul is talking about—not "the percentage of Jews who are holy".
Paul is not making illustrations to explain Israel in these verses; he is creating an illustration to explain that grafted branches (Gentiles), though not genetic, are just as dependent on the root system as the natural branches (Israel).
Romans 11:17-18 (NASB)
17 But if some of the branches were broken off, and you, being a wild olive, were grafted in among them and became partaker with them of the rich root of the olive tree, 18 do not be arrogant toward the branches; but if you are arrogant, remember that it is not you who supports the root, but the root supports you.
After that hermeneutical diligence, we can answer your question directly...
Many in Israel were "broken off [branches]", making room for the Gentiles. Again, Paul says this clearly, but then redirects his point to be in awe of God, not to wonder who is better than who.
Romans 11:20 (NASB)
Quite right, they were broken off for their unbelief, but you stand by your faith. Do not be conceited, but fear;