This isn't true as a matter of historical fact. The contemporary nation-state of Jordan was established in 1946, prior to the U.N.'s partition plan for Palestine. There was no expectation at that time, for those Palestinian Arabs living west of the Jordan River -- who were themselves the descendants of people who had been living in that land for multiple generations -- that this then-new nation-state of Jordan was to be "their country" going forward. That's a myth.
There were, of course, Jews living throughout Mandatory Palestine as of 1947, and they, too, were the descendants of people who had been living in that land for multiple generations. But as of 1947, Palestinian Jews were a minority in every region of Palestine with the exception, I believe, of Jerusalem itself and its immediate environs. The 1947 U.N. partition plan established the borders of what would be the new nation-state of Israel based on those areas of Palestine that had the largest concentration of Jews (albeit, still in the minority relative to the Palestinian Arab population, even though non-native European Jews had started to emigrate into Palestine as early as post-WWI, if not earlier, as part of the Zionist enterprise).
Given this, in what way can those Palestinian Arabs currently living west of the Jordan River, descendants of those who for multiple generations had always lived in Palestine west of the river, be considered to be "Jordanians"? Again, this notion that "Jordan is the Palestinian state" is a myth and, at this point, an intentional misdirection.
Now, if somebody wants to switch gears and resort to the Bible to make the claim that "Israel rightfully belongs to the Jews," so be it. Or if, at this point, somebody wants to resort to the assertion that the "Israeli Jews" are entitled to the land outside the boundaries established by the U.N. partition plan because they "won it in a war," well, so be that too. But those are different, um, arguments.
Yeah, that would be me.
That ignores the ongoing agreements among the nations before 1946. Read about the British Mandate at https://www.britannica.com/place/Palestine/World-War-I-and-after#ref45067.
"Although Transjordan—i.e., the lands east of the Jordan River—constituted three-fourths of the British mandate of Palestine, it was, despite protests from the Zionists, excluded from the clauses covering the establishment of a Jewish national home. On September 29, 1923, the mandate officially came into force."
Basically, Israel and Transjordan were created at that moment as a 2-state solution, but with no decision yet regarding who'd be in charge.