H.W. Bush was pretty strong when it came to Middle Eastern foreign policy, and given the outcome of the Gulf War and the subsequent liberation of Kuwait, it's understandable that his administration wanted to address other conflicts in the region, like that between Israel and Palestine.
Of course, despite the delay on this dialogue, I don't think that the outcome would have gone any more smoothly, even without the hiccup as described. The Palestinian leader was outspoken and honest in his support for Saddam Hussein, who being the leader of Iraq, was the U.S.'s primary enemy in the Gulf War.
H.W. was also honest in stating that relations between Palestine wouldn't improve with such a stance. To quote Bush himself regarding Palestine following the dialogue:
To me, they've lost credibility. They've lost credibility with this office right here. And the reason they have is that they behaved very badly to those of their own fundamental faith.
Though, it is worth mentioning that he didn't lose all faith in attempting to broker peace. Another quote from Bush:
In the Middle East, we're close to convening a conference this October that will launch direct talks among Israel, the Palestinians, and the Arab States. I welcome Prime Minister Shamir's statement that he supports our proposal, and I call upon Israel and the Palestinians to clear away remaining obstacles and seize this truly historic opportunity for peace.