Soon after the war that secured Israel's independence and status ended the country moved its government to the western portions of Jerusalem under its control and declared its capital to be Jerusalem, where it remains to this day. It didn't matter that Jordan occupied much of Jerusalem. The central government buildings and staff were located in Jerusalem, just not in the occupied section. They didn't have what they wanted; they settled for what they had.
The primary problem is that one little raised bit of ground is the first holiest site in Judaism. And after the Jordanians agreed to equal access for Jews, they reneged and didn't let Jews near the Temple Mount. Rhetoric out of the Palestinian side, Arab capitals, and even the UN deny any connection between Judaism and the Temple Mount. Some see this is providing justification for just such prohibitions past and future. Past actions and present rhetoric easily say the same thing--in fact, it's hard to see how present rhetoric provides any sort of guarantee or even grounds for negotiating as equals. "It's our third most sacred site, but meaningless to you" is hardly an even-handed approach. One wonders what others think the real basis for the Jews' thinking they have a connection to the site is.
To some extent, it's a re-revision of patently revisionist history that'll be needed between there's any broad acceptance of sharing the site. Loss aversion, though, is a mighty force to contend with, and now we have it on both sides.