Amartya Sen, admitting he was "astonished", told NDTV "it shows the country is in the hands of an authoritarian regime pursuing its own view of what is good for the country".
The cow, he remarked, "isn't one of my favourite words" but it was not about that. "I think what they object to is the particular statements, it's not that they didn't like my reference to Gujarat but it is to what happened in 2002," he said.
Suman Ghosh, a national award-winning filmmaker who teaches economics in the US, said the censor board's members watched his one-hour film for over three hours in Kolkata yesterday. After that, they said his documentary would be released with a UA certificate - requiring parental guidance - if he agreed to blip out the words.
"I was quite shaken. I was shocked but I thought, I have to argue," Mr Ghosh, 44, told NDTV, emphasising that he would not compromise and was ready to fight all the way to court.
"The film was my comment on India. I feel disheartened because I wanted to convey certain thoughts and they are trying to stifle it...I have heard that these things are going on. Now I have a taste of this first-hand."
If the filmmaker wants to contest the board's decision he has to appeal to a review committee and then go to a tribunal. His final option is the court.
Filmed over 15 years, the documentary has Dr Sen in conversation with one of his students, economist Kaushik Basu.
It has already debuted in New York and London. It was screened in Kolkata for the first time yesterday, but further shows in India are in question now.
The censor board headed by filmmaker Pahlaj Nihalani - a vocal supporter of the ruling BJP - is familiar with controversies. It has reportedly asked for multiple cuts in "Indu Sarkar", a film on the Emergency.
Earlier, it asked directors to remove all references to Punjab in the movie "Udta Punjab" on the state's drug problem.
The board also blocked "Lipstick Under My Burkha", telling its director the story is "lady oriented", has continuous sexual scenes and abusive words.