On Wednesday, Jenkins called a critical fan a "retard" when taking exception to questioning about why the stats Jenkins was using to showcase his effectiveness weren't contributing to victories.
Jenkins said Thursday that the usage of the word was "slang" that is "just part of my culture."
Giants coach Pat Shurmur met with Jenkins on Wednesday and said in a statement Friday that Jenkins' refusal to admit that what he did was wrong led to his release.
"This was an organizational decision," Shurmur said. "From ownership to management to our football operations, we felt it was in the best interests of the franchise and the player. Obviously, what happened this week, and the refusal to acknowledge the inappropriate and offensive language, was the determining factor."
Giants players found out about Jenkins' release in the locker room before their morning practice. They were well aware about the comment and saw his interview Thursday.
Jenkins did not have an opportunity to address his teammates after his release.
"It was an unfortunate situation," safety and captain Michael Thomas said. "It's unfortunate. It's unfortunate."
Jenkins, 31, had one year and $11.25 million remaining on his contract. A team can claim him for the final two weeks plus the playoffs for $1.2 million after Jenkins was officially listed as being waived/injured, as he had been recovering from an ankle injury suffered Monday night against the Philadelphia Eagles.
He has 54 tackles this season and is tied for fourth in the NFL with four interceptions.
This marks the official end of the Giants' much-ballyhooed 2016 free-agent class, as defensive end Olivier Vernon was traded this past offseason and defensive tackle Damon Harrison was dealt away last season. It was always a surprise that Jenkins had lasted this long under the current regime. General manager Dave Gettleman prioritized improving the team's culture from the start, jettisoning seemingly everyone deemed part of the problem.
But Jenkins remained, despite being suspended during the 2017 season for knowingly failing to return from the bye week on time. He criticized the pass rush earlier this season -- noting he can't cover for eight seconds -- and was critical of defensive coordinator James Bettcher in recent weeks for not using him to shadow other teams' No. 1 receivers. The Giants (2-11) still raved about Jenkins, even mentioning him as a team leader for the younger group of cornerbacks.
"Rabbit is a good guy. He's a good person. He's a good man," Gettleman had said of Jenkins. "He wants to win. He's not stupid. He knows that these young kids, these young corners -- DeAndre [Baker], Sam Beal, Corey Ballentine and Julian Love -- they have to grow up quick. He's more than happy to help them along."
It didn't stop Jenkins from making the inappropriate remark that didn't sit well with the Giants.
"It's not a word that you should use. I made that very, very clear [Thursday]," Shurmur said. "I made it clear to him as well."
Jenkins originally apologized on Twitter for the comment after meeting with Shurmur on Wednesday afternoon.
"I really didn't seem so bad with it," Jenkins said. "People like y'all started picking it up and making stories. So I just apologized."
He then apologized at the start of his news conference Thursday, but it later became obvious that it was mostly hollow.
"I regret it. But at the end of the day, it's my slang," Jenkins said. "So if you take it how you're going to take it, it's on you. I don't mean to offend nobody. My dad always told me, 'Speak freely and own up to what you say.' So I always speak freely as a man, and I speak how I want to speak."