Bobby Storey was a former leader of the IRA and at the time of his death last year he was a prominent member of Sinn Fein.
The man, referred only as Mark from Lisburn, made the remarks live on The Stephen Nolan Show on BBC Radio Ulster on Friday morning.
Mark, who described himself as "completely neutral", recounted how he and his three children had to stay home while his wife/their mother was one of five people allowed to attend her grandfather's funeral at the beginning of April.
Irish republican rebel band Wolfe Tones lead giant Belfast crowd in singing Up the Ra ‘on the same night as singing Give Peace a Chance’
Larne FC suspends player John Herron after he was spotted on camera wearing ‘tiocfaidh ar la’ assault rifle top
‘He needs to leave our club NOW!’ Strong reaction Larne FC’s John Herron being pictured in ‘tiocfaidh ar la’ gun top as club suspends him
Feile organisers asked if they have warned Wolfe Tones about leading young people in pro-IRA chants
Feile 2022: Tourism NI indicates it could pull funding for West Belfast Festival unless organisers live up to ‘responsibility to promote good relations’
"I don't know who Bobby Storey was," said Mark.
"Mr. Storey deserved a funeral but he didn't deserve a better funeral than my grandfather-in-law - I want to know why he was more special than the eight families who said goodbye to their loved ones at Roselawn Crematorium on the same day."
Mark went on to ask deputy First Minister, Michelle O'Neill, who attended Mr. Storey's funeral on June 30, 2020, to meet him and tell him why "their friend (Bobby Storey) was more special than my grandfather-in-law".
"I respect every party for what they have done for Northern Ireland.
"I loved seeing Martin McGuinness and Ian Paisley laughing on the TV - see our future going forward and our greatness.
"But this hurts to the bone so I say this to Michelle O'Neill or Conor Murphy to meet me on the steps Stormont today and they can tell me to my face why their friend is more special than my grandfather-in-law - but they won't because they are a bunch of cowards."
An independent investigation into how Belfast City Council permitted up to 30 mourners to gather inside Roselawn Crematorium for the cremation of the remains of Bobby Storey while eight other families who said goodbye to loved ones on the same day were treated differently.
The report was carried out by Peter Coll QC.
Mr. Coll QC said he found no evidence that Sinn Fein exerted pressure on Belfast City Council to treat Mr. Storey's cremation different to the eight other families who said goodbye to loved ones at Roselawn Crematorium on the same day.
A message from the Editor:
Thank you for reading this story on our website. While I have your attention, I also have an important request to make of you.
With the coronavirus lockdown having a major impact on many of our advertisers — and consequently the revenue we receive — we are more reliant than ever on you taking out a digital subscription.
Subscribe to newsletter.co.uk and enjoy unlimited access to the best Northern Ireland and UK news and information online and on our app. With a digital subscription, you can read more than 5 articles, see fewer ads, enjoy faster load times, and get access to exclusive newsletters and content. Visit https://www.newsletter.co.uk/subscriptions now to sign up.
Our journalism costs money and we rely on advertising, print and digital revenues to help to support them. By supporting us, we are able to support you in providing trusted, fact-checked content for this website.