"She is furious that he shared something so private."
The source added that Kardashian West's main concern is how her husband's revelations about their private life may affect their four children (North, 7, Saint, 4, Chicago, 2, and Psalm, 1).
"She loves her kids tremendously and wants to protect them," they said.
A second insider told People that the couple's relationship has begun to suffer due to West's behavior.
"Things have broken down significantly between the two of them, and it's happened pretty suddenly," the insider says.
Sources also told TMZ that the family are "shocked beyond words" by the Grammy-award winner's personal revelation and feel he is in "desperate need of professional help" for what they claim is a bipolar episode.
During the first rally of his presidential campaign at the Exquis Event Centre in South Carolina, West broke down in tears.
He did not bring a microphone, and instead repeatedly told the crowd to "be quiet" while he was talking.
The rapper grew emotional during a monologue on the issue of abortion, revealing that he and Kardashian West considered not having their first child, North West.
"In the Bible it says thou shalt not kill," he said.
"I remember that my girlfriend called me screaming and crying. At that time I was a rapper, I was out there, I had different girlfriends. Hey I don't give a f***. So my girlfriend called me and I just thought to myself, please don't tell me.
"And she said I'm pregnant.
"For one month and two months and three months, we talked about her not having this child. She had the pills in her hand. If you take it, the baby's gone.
"I was sitting up in Paris, and I had my leather pants on. I'm in the apartment where my wife was actually robbed, and I got all my creative ideas ... and the screen went black and white, and God said if you f*** with my vision, I'm going to f*** with yours."
Eventually West reached his point, saying abortion should "always be legal", but there "should be an option of maximum support".
His idea, which he called a "maximum increase", was to give every woman the option of taking a large payment from the federal government to help her raise her child.
He mentioned the policy a couple of times – the first time, the proposed payment was US$50,000, and after that it became US$1m.
"Everybody that has a baby gets a million dollars, or something like that," he said.
West kept speaking about abortion for some time, offering his version of a counterargument to the pro-choice slogan "My body, my choice".
"Women love 'My body, my choice'," said West.
"Let's say, when the baby is conceived, at that point it has a soul. That's a real, living thing."
He then launched into a hypothetical scenario in which a couple were separated, and had a child together, who was living with the mother.
"She says, 'My house, my choice. I'm gonna kill my child.'" he said.
That comment prompted gasps and groans from some in the audience.
"I did smoke a little bit last night," West added a short time later.
"And I called my wife and she said, 'We're going to have this baby.' I said, 'We're going to have this child. I know people that are 50 years old that never had children, that have never been able to experience the level of happiness that I experienced.
"My mum saved my life. My dad wanted to abort me. My mum saved my life. There would have been no Kanye West, because my dad was too busy!"
At that point West started to cry, and it became difficult to discern much of what he was saying.
"I almost killed my daughter! I almost killed my daughter!" he shouted.
"We love you Kanye!" some members of the crowd shouted back.
That was followed by a string of mostly unintelligible sentences.
"They're going to run this, they're going to try to tell you that I'm crazy. The world's crazy," West said.
