However, the well-known writer and campaigner was taken aback at the tone and frequency of the broadcaster's interruptions.
"I was taken aback by the extreme rudeness and wearied by how difficult it was to conduct the interview," Ms McKay said.
"He was ridiculing what I was saying."
When Ms McKay pointed out that there was only a small percentage of women in the Dail, interviewer McGurk said that her views were outdated.
He said: "I honestly don't understand this. Are you suggesting that if half the Dail was female and half was male we'd be better off?"
"I think you're living somewhere like 1974."
He added: "It's just as well it wasn't a male politician who got rid of the cervical cancer vaccine, wasn't it?"
Ms McKay, a well-known journalist and author of several books, said that she had not anticipated to be treated in this manner.
"An interviewer is there to elicit the views of the other person," she told the Herald.
"Of course they should always challenge them, but that's not the same as talking over the response."
On the show, broadcast on July 29, the director of the National Women's Council spoke out and told Mr McGurk that his interruptions were "very tiresome".
He replied: "Oh, I'm sorry. I'll give you 30 seconds to say what you want to say."
She replied: "What I want to say I've already said, but unfortunately it may have been very difficult for the listeners to hear it because you talked over practically every single thing that I said, which you probably think is a very provocative and interesting way of doing an interview, but I don't think so at all."
Mr McGurk asked her if that was because he was a man -- but McKay responded by saying: "It may be or it just may be that you're a particularly rude man."
Researchers at 4fm have since asked Ms McKay to speak on another show, but she has turned them down.
"We have decided that we are not going to give any more interviews to 4fm," she said.
"We are a serious organisation and we have a point of view that we want to put across. We are not going to expose ourselves to be treated in that uncouth and objectionable manner."
A spokesperson for 4fm said that McGurk on 4 aims not only to report the issues of the day but also to discuss them, in an honest and frank way.
The spokesperson said: "Tom McGurk is a very passionate personality and, as his fans will know, he is always vocal about his opinions.
"Never one to shy away from a challenging topic, Tom will converse with his interviewees as he would his friends -- and if he disagrees with you, he will let you know."