I am not making such arguments. It's you not even bothering to prove Jesus was a Jew because you can't. You need to believe it.
Iesus Nazarenus Rex Iudaeorum
Iuda DOESN'T mean jew.
Iudaeorum translates inhabitants of Iudaea. However Not everyone who lived in Iudea was descendant of Iudah/Judah. Jesus was king of the nation therefore. Not of race of jews we know today they did live there too however, or rather say their direct ancestors who killed Jesus.
Jews as we know them today are of Khazar origin.