The quote you’re using is from the 2010-2011 peace talks. The reason those broke down is as follows:

Direct talks broke down in late September 2010 when an Israeli partial moratorium on settlement construction in the West Bank expired and Netanyahu refused to extend the freeze unless the Palestinian Authority recognized Israel as a Jewish State, while the Palestinian leadership refused to continue negotiating unless Israel extended the moratorium.[3] The proposal was rejected by the Palestinian leadership, that stressed that the topic on the Jewishness of the state has nothing to do with the building freeze. The decision of Netanyahu on the freeze was criticized by European countries and the United States.

In regards to Oslo and the 2014 peace talks:

2014:

A deadline was set for establishing a broad outline for an agreement by 29 April 2014. On the expiry of the deadline, negotiations collapsed, with the US Special Envoy Indyk reportedly assigning blame mainly to Israel, while the US State Department insisting no one side was to blame but that “both sides did things that were incredibly unhelpful.”

Oslo: Both Oslo accords were signed, however,

the interim process put in place under Oslo had fulfilled neither Israeli nor Palestinian expectations.

This led to the Camp David Accords where the main issues and points seemed to be the following:

the refusal of the Palestinians and Arafat to give up the right of return

Judged from the perspective of Palestinians’ and Israelis’ respective rights under international law, all the concessions at Camp David came from the Palestinian side, none from the Israeli side.

the Palestinians starting position was at the 1967 borders, but they were ready to give up Jewish neighborhoods in East Jerusalem, and parts of the West Bank with Israeli settlements. Further, the Palestinians were willing to implement Right of Return in a way that guaranteed Israel’s demographic interests.

The proposals were, for the most part, verbal. As no agreement was reached and there is no official written record of the proposals, some ambiguity remains over details of the positions of the parties on specific issues.

The talks ultimately failed to reach agreement on the final status issues: Territory, Territorial contiguity, Jerusalem and the Temple Mount, Refugees and Palestinian right of return, Security arrangements, Settlements

To summarize the 2010-11 peace talks broke down due to Israel not abiding by the terms of the negotiation. The 2014 talks are debated with more blame seeming to be placed on Israel. The Oslo accords were signed but left unresolved and unfollowed by Israel leading to the camp David accords where the main issue seems to be the right of return for the hundreds of thousands of Palestinians who were displaced. However, who actually ended the talks is still debated.