Robin Scott-Elliot: An Open venue closed to women does Scotland no favours at all

There is no sign of change at St Andrews or Muirfield or Troon

For the stout-hearted this is a good time of year to play Muirfield, providing you wrap up warm – the wind that howls off the Firth of Forth and on to Scotland's gently undulating east coast can feel as though it has not paused for breath since leaving the Arctic.

Muirfield hosts The Open later this year, the 16th time the grand old course has entertained golf's most venerable event. At this time of year, when there is the first sign of light at the end of winter's dark tunnel, green fees are reduced – it's £110 to play one of the world's great courses, a saving of £85 – and there are tee times available as the men who make up the Honourable Company of Edinburgh Golfers are sensible enough to stay indoors until it warms up properly and the wind drops from storm warning to a gentle gale force.

So they remain swaddled in their distinctive clubhouse that sits on the edge of the 18th green where Ernie Els was crowned the last time The Open was here 11 years ago. The building resembles an erratically extended suburban home and houses views that belong in a suburb frozen in Victorian times.

The Honourable Company does not allow female members. It's a standing it has in common with three other Open venues, Royal St George's, host in 2011, the daddy course itself, St Andrews, where the Championship will be determined in 2015, and Royal Troon, set to hold the event in 2016, a big year for the sport with its inclusion in the Rio Olympic Games.

Last year's London Olympics were a high water mark for women's sport. For the first time every nation sent male and female athletes to walk together in the opening ceremony. Sarah Attar, the first Saudi woman to run at the Games, could not become a member at Muirfield. Nor of Troon, St George's or St Andrews. If the London opening ceremony did so much to accentuate areas of this country's progressiveness, then the attitudes exercised among the Honourable Company and their ilk make that a good work spoiled.

This sporting summer it will be back to basics – uneven years mean no Olympics, (men's) European Championship or World Cup, so those foundation stones of British sport Wimbledon and The Open reclaim unbroken attention. They are great events, given their standing by layers of history. But they have to move with the times. Wimbledon settled its contentions around equality five years ago, agreeing equal prize money for men and women.

Last year Augusta, a club that put the small "c" into conservative, decided it would admit female members. It was a move "noted with interest" on this side of the pond. But there is no sign of any change at St Andrews or Muirfield, or Troon. "It is not an issue for the outside world," is the response from Muirfield when the subject is raised. It is a private members' club and it is for its members to determine who should be allowed to become one. It's a legally watertight defence for an antediluvian attitude.

The Scottish government will be using The Open's return to push its country's cause, as it will do with the Ryder Cup and Commonwealth Games the following year. High-profile sport comes with add-ons these days, visitor numbers and tourist dollars. That is important to Scotland. But it is also important for the country to be seen as the progressive nation that it, by and large, is. The attitudes of all three of these private members' clubs are a wider embarrassment and should be flagged up and derided at every opportunity.

"It is not a big-ticket event for the club," is how Muirfield's secretary, Alastair Brown, puts hosting the event. The suggestion is that the club is gracing the world with its presence, doing us a favour by opening its doors for The Open.

If they don't really want us there this summer, there is another significant sporting event happening at the same time, the women's (or ladies', to use Muirfield's preferred parlance) football European Championship. England are there – Scotland came honourably close to qualifying – and will have a chance of winning it. The BBC is showing games on BBC2 and 3. The Open will be over on BBC1 with that prime-time finish on the Sunday evening. Perhaps The Open would be best hidden behind the red button and prominence given instead to the women's football.

The BBC has made a positive effort to broaden coverage of women's sport since the Olympics – an area in which all sections of the media have been found wanting – and what better signal to send that the world has changed?