"Just talking with my family, that was the most important thing," Williams told ESPN.com in a phone interview from his offseason home outside Dallas. "And also, just the fact that they didn't have anybody experienced enough behind Kyrie [Irving]. We have Jordan [McRae] and we have Kay [Felder], and those guys are going to develop and they're going to be really good, but they need some experience.
"I just thought about repeating, thought about another championship, and I didn't want to put the Cavs in a situation where [they didn't have a] guy [who] could come in and play 5-10 minutes that could help them win and be a difference. I didn't want to put the Cavs in that situation at the end of the day."
Williams announced his intention to return Wednesday on Twitter.
Cleveland lost its primary backup point guard from last season, Matthew Dellavedova, in the offseason after he signed a four-year, $38 million deal with the Milwaukee Bucks. Before Dellavedova's departure, the Cavs paid $2.4 million on draft night to acquire a second-round pick and draft Felder, a 5-foot-9 guard out of Oakland.
McRae, called up by the Cavs from the D-League in February, is traditionally more of a scorer but has been developed as a point guard in the offseason for his defensive potential at the position.
Williams exercised his $2.2 million player option for 2016-17 back in June, but with the Cavs unsure of his health status, the team considered waiving his contract under the "stretch" provision, allowing them to spread out the money owed, or finding a trade partner for the one-time All-Star during the offseason.
Williams, who will turn 34 in December, confirmed to ESPN.com that chondromalacia, an irritation of the cartilage under his left kneecap, caused him to consider retiring in the middle of last season and again after the NBA Finals once Cleveland came back from a 3-1 deficit to beat the Golden State Warriors.
"Physically I've been dealing with this knee for four years, so it's nothing new," said Williams, who received a platelet-rich plasma injection in the knee before the playoffs that helped ready him to be a spot contributor in the postseason. "It just got to the point where it's like a cup of boiling water. If you turn it up high enough, eventually it will boil over.
"It just got to the point where my knee was bothering me a lot and, s---, we won the championship, man. That's my ultimate goal. That's all I ever wanted as a basketball player and when I conceded that aspect of it, that really my basketball life was fulfilled at that point. So it made the decision for me to walk away from the game a whole lot easier being that my boys are growing up and I want to have that time with them."
Williams told ESPN.com that he did not consult with coach Tyronn Lue, general manager David Griffin or anyone else on the Cavs about his decision to return.
LeBron James posted a photo of the team's voluntary minicamp at the University of Santa Barbara on Thursday, and Williams was the only Cavs player under contract not in attendance.
Free-agent guard J.R. Smith, whose contract negotiations with the defending champions have stalled, was also not present.
Williams is spending what's left of the offseason with his family and training at his eponymous gym, the Mo Williams Academy, before reporting to Cleveland for training camp next week.
"What I'll bring to the Cavs is what I do: I'll back up Kyrie, spell him some minutes and obviously do what I always do," Williams said. "But my thing is these young guys coming up, like a Jordan, like a Kay and even Ky -- he's growing into that player that we always knew he was going to be -- but at the end of the day, just being around those guys I'm able to bounce back 14 years that I've had to them guys with no hidden agendas. I can only enhance them and help their progression."
In the meantime, Williams says he looks forward to receiving his championship ring Oct. 25, when the Cavs host the New York Knicks on opening night.
"Obviously we're going into another season and we're going to be the defending champions. And as hard as it was to get it done last year, we should be able to come in with a lot of confidence, a lot of camaraderie, a lot of guys coming back that were on the team last year," Williams said. "I feel like mentally we're in a good place as a team. Obviously we've got the ultimate confidence in T-Lue and his staff, and I feel like we have two of the best players in the world on one team. So, I think we're in good shape."