When I found that article initially, I did some commenting back and forth with the author, and at one point found myself speculating on what my side of the coin might be. Is there something just as obvious that would make my interactions with other people generally/men in particular that much easier? I didn't come up with anything at the time, but I think now I have. I'm going to continue using the gender roles as in the original, a shorthand for people who think and behave in the ways described (so chosen because of the large overlap between those groups and the two genders).
My theory is based on the idea that women read volumes more connotations into interpersonal interactions than men do, which is not in and of itself revolutionary. But when miscommunications inevitably occur as a result, I think the men get blamed more often than is fair. Women and others who interact as I describe, consider: you're in a better position to prevent this than he is. You can't create in his mind all the associations and implications in yours, but you CAN be conscious that he's not aware of them and adjust your expectations accordingly. Be direct. Say, don't imply. Use clear and simple language. By no means am I saying to be condescending or treat him like a neanderthal. You can do this politely and respectfully, or crassly but amiably if that's what's called for.
"Say what you mean" isn't a good way to put it. You always think you're saying what you mean--otherwise, why would you have said it that way? A better explanation is that you need to listen to the actual words you're using and consider whether they represent all of what you want to communicate. Obviously you can use some implications and references, or language would be impossible. But if you're trying to tell someone what you want, don't say something which you know you wouldn't say unless you wanted it. Just tell him what you want. It will not occur to him to interpret the other way that deeply.
Now the next interesting question is, why don't women already do this? It's not difficult, and it comes up often enough. I think this is a combination of two factors: first, as already mentioned, we have these connotations and layers of meaning in our heads already and it doesn't occur to us that anyone else wouldn't. Second, we use indirect language as a form of diplomacy--"I would like" is more polite than "I want," and so forth. With that so deeply ingrained, it feels rude to state things outright, especially when they relate to desires or dissatisfaction or other statements with potentially negative responses. Here's the great thing, though: this solution works on that phenomenon. The same guys who don't read everything you want them to into your indirect speech won't read rudeness into your direct speech.
In short, men hear and understand what women say, not what they mean. Naturally there is a mismatch between these two things, but there doesn't have to be. It just takes some thought and genuine attention to the words you're using to represent what you want to convey.