John 1:24 And they which were sent were of the Pharisees. 1:25 And they asked him, and said unto him, Why baptizest thou then, if thou be not that Christ, nor Elias, neither that prophet?
John 4:9 Then saith the woman of Samaria unto him, How is it that thou, being a Jew, askest drink of me, which am a woman of Samaria? for the Jews have no dealings with the Samaritans.
John 4:22 Ye worship ye know not what: we know what we worship: for salvation is of the Jews.
Seems to me you are off on your above about the Pharisees having a problem with a Jew being water baptized.
That first verse is the one I would have cited you in support of my point. I don't see how the other verses are related?
Some questions...
Why did the Lord refer to Nathaniel as an Israelite indeed?
As nearly as I can tell, it was a recognition of the virtue already present in him. But that's just at a reading, right now. I haven't ever contemplated it before. If you have something to teach, by all means...
Why does Paul refer to himself as an Israelite and a Jew?
Paul was from the tribe of Benjamin, which was part of the southern kingdom. Thus, he was a Jew because he was from Judah.
He was an Israelite in the larger sense - that he was a descendant of Abraham, as it says in the verse.
The nomenclature can be confusing, because
Israel can refer to either all the tribes, during their united period, or it can apply only to the northern kingdom. In many places, when the northern kingdom alone is meant, the phrase used is "house of Israel" rather than just "Israel." E.g. I am sent only to the lost sheep of the house of Israel.
Why does Paul use either label when referring to Jews and Israelites he is dealing with and or writing about?
I don't think he does. He begins several addresses with "men of Israel," but it appears to me that he has thus addressed his speech, because he is speaking to those who he anticipates will receive his word, or those who already have. "Jews," by contrast, is used wherever the opposite is the case, as in Acts 13:50.
Where is it in Scripture that water baptism is an adoption ceremony?
John 3 - Jesus interaction with Nicodemus. You must be born again. What do you think "born again" means, if not adoption? Nicodemus wasn't sure, so Jesus spells it out for him... born of water and of the spirit. Is there any doubt that baptism is what it is view?
But really, the people in that day didn't need that explained to them, just as we don't need someone to explain that a wedding is a ceremony of marriage. The author of Hebrews says, "let's not go over the basics, like baptism, again..."
If you really wish to see it spelled out, there are some papyrii from the 1st century that describe the practice.
Alternately, ask your local rabbi about the process to become a Jewish proselyte. The Jews
still baptize their converts. They baptize "in the name" of Abraham, meaning to add the proselyte to Abraham's family tree.
Let me break it down for you visually. A baby resides in the mother's womb, which is full of water. At birth, the water breaks, and the baby exits into the world. In baptism, one is brought underwater, and then made to come up and out. It's a picture, or re-enactment, of birth. Re-birth. The new birth. Born... again.
Thanks for asking the question.