One of the particular challenges that real men manage to overcome is the challenge of keeping his temper in check. Whether arguing with a spouse, a mate, or a child, even when dealing with a naughty pet, it is never a sign of anything good when a man loses control of his temper.
Meekness is the characteristic of "restrained/reserved strength". Just because you have the physical ability to dominate, doesn't mean that you should. A reign of terror, in which you keep everyone in check by fear of what you will do or say to them, is not cool. It's good for those whom you lead to realise that you have that power though - it leads to greater respect when you keep your cool and ask for obedience (rather than demand).
Restraining your anger is not the same thing as not letting people know that you are angry either. They will likely see it in your face anyway, but it is better if others trust you to keep control and seek justice through fair and careful means (rather than through a general explosion which has collateral damage). It may mean that your brain feels like it will explode, especially if you are clearly in the right, but let the pressure out with a deep breath and act wisely. Your head will remain intact!
Part of a real man's burden is to suffer wrong at times too. More on that another time.