Kevin Durant and Kyrie Irving were expected to make the Nets instant title contenders when they joined the team in 2019, bringing two of the best offensive talents in the N.B.A. to a team that had just finished sixth in the Eastern Conference.

But three years later, without any championships or finals appearances with the Nets, Durant and Irving spoke Monday about a rocky off-season that at times seemed like it might end with both of them playing for other teams.

In June, Durant, 33, requested a trade, which he said Monday was because of uncertainty and accountability issues in the organization.

“I want to be in a place that’s stable and trying to build a championship culture,” Durant said. “So, I had some doubts about that.”

Despite his trade request coming just days after Irving and the Nets couldn’t agree to a long-term extension, Durant said that wasn’t a factor.

Instead, he pointed to the Nets’ 11-game losing streak while he was injured last season as a worrisome signal about the team’s direction. At the time, he didn’t want his concerns to affect the team’s play on the floor, he said, so he waited until the off-season to make his trade request.

“That’s what was putting doubt in my mind, is that when adversity hit can we keep pushing through it?” Durant said. “I’ve been on championship teams. I’ve been on teams that have been right on the brink of winning a championship, and they did those things. So, I want to be a part of a group that did that.”

He added: “Winning and losing — I can take all that. I’ve been in the league for a long time. So, it’s not more so about just a result. It’s like how we get to that point. And I wasn’t feeling how we was getting to that point.”

In August, The Athletic reported that Durant had told the Nets to choose between keeping him or keeping General Manager Sean Marks and Coach Steve Nash. The report drew the Nets’ owner, Joe Tsai, to release a statement of confidence in the Nets’ leadership. “Our front office and coaching staff have my support,” Tsai wrote. “We will make decisions in the best interest of the Brooklyn Nets.”

On Monday, Marks said, “That’s pro sports, right?” He added: “Everybody’s entitled to their opinions. And I think from us, it’s not to hold a grudge against what Kevin said, but it’s almost like: All right, that’s the way he feels. What’s going on here? Like, what do we need to change?”

Nash said that he didn’t take it personally. “This is not new in the N.B.A.,” he said.

“Kevin and I go way back,” said Nash, who worked with Durant in Golden State as a team consultant. “So, you know, families go through things like this.”

The Nets shopped Durant to other teams, but on Aug. 23, Durant and the Nets announced that they had “agreed to move forward with our partnership.”

Durant said he wasn’t disappointed or surprised to return to the Nets: “I know I’m that good that you just not going to give me away.”

Before Durant’s trade saga began, there was the issue of Irving, whose contract negotiations and unwillingness to be vaccinated against the coronavirus dominated headlines for much of the past year. Irving said he felt as though the Nets had given him an “ultimatum.”

“I gave up four years, 100 and something million deciding to be unvaccinated,” Irving said. “And that was the decision: It was contract, get vaccinated or be unvaccinated, and there’s a level of uncertainty of your future — whether you’re going to be in this league, whether you’re going to be on this team. So, I had to deal with that real-life circumstance of losing my job for this decision.”

Irving, 30, was eligible for max contract extensions worth up to about $245 million, but he and the Nets did not reach an agreement on one. Instead, Irving opted into the final year of his contract, which will pay him $36.5 million this season. He said he had other options — but not many — and decided that staying in Brooklyn was the best choice for him. Irving played in just 29 regular-season games in 2021-22, mostly because he was ineligible to play at home because of local vaccine mandates.

Marks said that not reaching a contract agreement with Irving was because of reliability, not Irving’s stance against the vaccine.

“There’s no ultimatum being given here,” Marks said as Nash sat next to him and nodded his head in agreement. “It goes back to wanting people who are reliable people, who are here, accountable — all of us. Staff, players, coaches, you name it. I’m not giving somebody an ultimatum to get the vaccine. That’s a completely personal choice. And I stand by Kyrie, and if he wants, he’s made that choice. That’s his prerogative completely, and I totally understand that.”

While the Nets were navigating Durant’s injury and Irving’s absences last season, they were also affected by the unclear status of guard Ben Simmons. Amid tensions in Philadelphia early last season, Simmons, 26, was traded to the Nets for James Harden in February. Simmons, who said he was dealing a lingering back injury and mental health concerns, has never played in a game for the Nets.

He appeared to be close to suiting up in the first round of the playoffs, when the Nets were facing elimination against the Celtics. “That day I was was supposed to play Game 4, I woke up on the floor,” Simmons said Monday. “I couldn’t move, could barely walk.”

Simmons had back surgery in May. He said he was cleared to participate in training camp, which begins Tuesday.

“I’m excited to play with these guys,” said Simmons, who hasn’t played in an N.B.A. game since Game 7 of the 2021 Eastern Conference semifinals with the Sixers. “I think it’s a good opportunity for us, and we have a lot to prove.”