If you want to get technical, historically, people have the right to land by virtue of conquest or discovery. Nations as geographic areas don' t really exist, people comprise nations.

Those same people exert control over boundaries, which are recognized until they are not. Some people including the Jews have laid claim to land by virtue of it being land given to them by God. But whether given by God or occupied by a people, land has been changing hands since humans first lay claim to it.

Today, the right of "ownership" by discovery is over and to a large extent was abused historically since many lands "discovered" were in fact already occupied by indigenous people.

So, that leaves the "right of conquest" by a people as the basis for determining the geographic boundaries of a nation.

However, to reduce the frequency of wars, increasingly nations have joined international associations of nations, which have attempted to suppress the use of "conquest" to determine a nation's recognized boundaries and instead establish recognized borders, the violation of which by one nation against another is grounds for all nations to come to the aid of the nation whose borders have been violated (as in Ukraine today).

So, when Israel is demanding Arab nations recognize its right to exist, it is essentially asking Arab nations including the Palestinians to recognize their borders and Israel as the legitimate government of the land within those borders.

Such recognition would extinguish any and all claims, that Palestinians have as a separate nation to those lands.

Historically, one of the biggest points of dispute between Israel and the Palestinians with respect to the "two state solution" has been the Palestinian refusal to recognize Israel's boundaries as "sovereign" and instead it has always tried to structure any peace as a suspension of hostilities rather than a permanent recognition of Israel's boundaries.

In simple words, the Palestinians are trying to keep their conflict as a "civil war" between two peoples of one nation at best or as a conflict whereby the Jews invaded their lands. They are simply unwilling to recognize the Jews historical claims to the land or its recent claims by right of conquest.

On the other hand, Israel is interested in establishing permanently recognized boundaries between Israel and a separate Palestinian state, but a condition of such recognition is Arab acceptance of those boundaries as not a division between one nation at war with itself but as a permanent boundary between two sovereign nations.