In the American church today, the standard philosophy when it comes to attracting men is that you set the barrier for entry as low as possible. You ask little to nothing from men, you don’t expect much from them by way of attention span or effort, and you try to make the service as much like a rock concert or sporting event as possible. In effect, we treat our men like Homer J. Simpson (a moron) or Ned Flanders (effeminate), and are then surprised when the competent men aren’t present.
What men are attracted to, however, is risk, danger, and the promise of reward. When men have real mission, real challenges, and a high barrier for entry, they are fully engaged.