In 1999 Dr Jerome Teelucksingh, an academic from Port of Spain, Trinidad, had an idea. He imagined one day of the year when the world would address male gender-specific problems and celebrate positive male role models. On the date of his late father's birthday, 19 November, he organised an event at Port of Spain University. In the 12 years since, International Men's Day (IMD) has spread to at least 50 countries, but despite winning the blessing of the UN, it is far from the best publicised or funded event on the global calendar. Indeed it probably comes as news to you that it is happening at all. But if you're lucky there may be activities happening close to you tomorrow.

So this week I posed a simple question to the hive mind of Twitter: what do you think of IMD? From the dozens of responses, a grand total of four were broadly supportive. The majority were dismissive, jocular or mocking, and about a quarter were actively hostile. Before conducting that unscientific experiment I had been ambivalent, but the balance of replies convinced me: IMD is necessary and deserving of support, precisely because so few people believe it is needed.

Inevitably, the commonest response was some variation on: "I thought every day was International Men's Day?" And I don't dispute that for 365 days a year, men dominate power structures and the public agenda. The media pores over the movers and shakers of politics, economics, entertainment, industry and sport – all of them disproportionately men. But my issue here is not who is doing the talking, but what they are (not) talking about. For individually or collectively, the one thing men rarely do is talk about our problems.

So what should be up for discussion on IMD ? Male-specific health issues are the most obvious answer, and it is fortuitous that IMD falls bang in the middle of Movember, the cancer charity tache-othon. Raising awareness and research funding for prostate or testicular cancer is uncontroversial. But the focus could be widened to include suicide rates and depression, sexual dysfunction, take-up of primary healthcare and early interventions.

Then there are the political issues: toleration of prison rape; child visitation and custody policy; underachievement of boys in education; death and injury at work; provision of domestic violence and abuse services to male victims – the list goes on.

This is all starting to sound a bit depressing, so let's look at the positives. There may be no shortage of celebrations of male sporting, entrepreneurial or political prowess, but wouldn't we all benefit from an annual opportunity to acknowledge the hands-on and stay-at-home dads, the charity volunteers, the community sports coaches? Or in a more traditional vein, those who risk their lives daily in the lifeboats and mountain rescue teams, or in the mines and on the merchant ships, doing the most dangerous and frightening jobs, often with scant recognition.

One of the great social and political challenges of the 20th century was to re-imagine and reinvent our working and domestic arrangements in line with changing gender roles. One of the greatest socio-psychological challenges of the 21st century is to create new models of masculinity, more in keeping with this new world. Much has been said – perhaps too much – about the supposed crisis of masculinity. Our gender identity is not in crisis but it is in flux.

There is plenty to admire and cherish in traditional masculine roles, from courage and strength to stoicism and self-sacrifice, and the key may be to find ways to incorporate the best of what we used to be with the best of what we would like to be. To do so requires opening spaces for discussion, not being afraid to lift the lid on some wormy cans, and talk positively about what it means to be a man. IMD might be a good place to start.

For this day to be fruitful, though, one ground rule must be observed by supporters and sceptics alike. These issues stand on their own merit, not in comparison to other causes in a hierarchy of injustice. Nobody suggests that World Aids Day somehow diminishes World Mental Health Day, or implies that Aids is a more pressing concern than cancer or malaria. People can celebrate all that is good about Irish culture on St Patrick's Day without anyone claiming it is an insult to the English or to the Welsh. The same must be true of IMD. Have a good day, fellas.

• This article was commissioned following a suggestion made by PeterJackson. If there's a subject you'd like to see covered on Comment is free please visit our You tell us page