"I believe in only two things completely. The First Amendment, and boobs," Mr Travis said, before nonchalantly carrying on with his argument.
"Wait, did you just say?" Ms Baldwin interjected. "Wait, hold on, hold on, hold on, I just want to make sure I heard you correctly, as a woman anchoring this show. What did you just say? You believe in the First Amendment and ..."
"Boobs," Mr Travis replied, emphatically. "Two things that have never let me down in this country's history, the First Amendment and boobs. So those are the only two things I believe in absolutely in the country."
At that point Mr Reed jumped in, berating Mr Travis for being a bit of an idiot. Ms Baldwin was still working out exactly what he had said.
"I just want to make sure I'm hearing you correctly, b-o-o-z-e, or b-o-o-b-s, because as a woman, I'm ..." she started to say.
"I said boobs. I believe in the First Amendment, and in boobs," Mr Travis reiterated.
"Why would you even say that on national television, and with a female host?" she asked.
"I say it live on the radio all the time, because it's true, and that's what I do. Because I like boobs and First Amendment, which is exactly what I said."
As her guests started to talk over the top of each other again, Ms Baldwin decided to abruptly end the segment.
"I'm done. I'm sorry, I'm done. I'm done, this is done. Conversation over, yanking mics. Bye. See ya," she said, before turning to address the audience.
"That was entirely inappropriate. Forgive me that it took a second, it's like, live television happens and you think you hear something, but you're not entirely sure, and then you realise it happened. So I apologise, for him ... and that."
The blow-up didn't end there though. As viewers ripped into him on Twitter, Mr Travis claimed CNN had already invited him back on, and pointed to what he believed was an example of the network's hypocrisy on the matter.
Ms Baldwin wrote an opinion piece for CNN's website, slamming Mr Travis and calling him "a guest we should never have booked in the first place".
"I just couldn't let this go," she said. "I quickly felt myself turning red, getting irritated and angry. My mind was racing. My face, I could tell, was incredulous. In the thick of it all, I could see my other guest, Keith Reed, was equally aghast.
"The newsroom around me fell silent. I was staring into the camera trying to make sense of what was unfolding on national television. I even caught my cameraman Jay's eyes in disbelief. I thought again: 'It is 2017, and this grown man on my show is talking with me, a female host, about boobs. Is this seriously happening?'
"This is not okay. Speaking to women like this is unacceptable. It is 2017. Why is this even happening?"
She ended her piece with one final jab at Mr Travis.
"As for my guest today - despite what he's tweeting, he won't be coming back on my show - ever."
But now Mr Travis has released a voicemail from CNN where he is asked back on the programme on Monday.
In the voicemail, the CNN staffer says the network "greatly enjoyed the conversation" with Mr Travis and invited him back on air.
"(We) wanted to see if you could use us for a continuation of that conversation on Monday," the woman says before leaving her phone number for Mr Travis to call back.
