Ownership of the land was a patch work. Much of the land was owned by absentee landlords who lived in places like Egypt, and farmed by local Arab Palestinians. This may have made many Palestinians believe it was "their land," but sorry, that just wasn't the case.
As the Zionist movement gained traction in the early 1900s, Jews around the world contributed to a fund to buy up tranches of land, and much of the land for the future Jewish state envisioned by the early Zionists was acquired this way. Once again, the poor Arabs living on and farming the land may not have been happy to give up the land they lived on, but it was not "stolen from them," because they didn't own it to begin with.