Communication is a skill like any other. It has to be learned. Some people are natural at it, but most of us just aren't. And men and women communicate in completely different ways, which makes understanding what's going on or really being said that much harder.
I do agree that counseling is really going to be needed to help you work on communication skills-- it's probably the #1 thing couples counselors do because most of the issues couples have are because of poor communicating, or not understanding what the other person is saying. We can hear the exact same words and not get the same meaning out of them, so it's important to clarify what that person actually MEANS.
There's a woman who's studied all of this and wrote a few books about how people communicate and listen. Her name is Deborah Tannen, and the first book I read was called "You just don't understand" it's about women and men in conversation. Total eye opener. There's another one called "That's not what I meant" which goes deeper into the misunderstandings people have when communicating.
There's also a type of counseling therapy called "Imago" therapy. It's a bit slow, and not my favorite, but what they do is that the couple will sit, looking at each other and one person will say what they need to communicate. The other person will sit for a minute, then repeat back to them what they think they heard. Then the first person will either say, yes that's what I meant, or correct them because that's not what I meant. There's a little more to it, and having a counselor there to catch things helps, but the basic concept can be applied by couples, especially when discussing difficult things.
That way, you sit and think about what you need to really say, and say it, and he tells you what he is hearing. He doesn't REPLY to it right away, he only tells you what he think you meant.
It can also help to clarify types of conversations (I am learning to do this with my hubs). Some examples:
"I am feeling a bit down and need to talk to you. I don't want you to try to fix anything, just listen to me, let me express it and hold me."
"I have some concerns about X. I need to express them to you and know you have heard me and are taking them into consideration. I do NOT need you to agree with my take on the situation, but I do need you to respect my concerns and at least listen to them without blowing them off."
And I, too, can get to crying during conversations and it's usually due to two things: My concerns are not being listened to and just blown off as me being "overworried", "jealous", or "not seeing things correctly", or my husband doesn't want to hear what I'm saying and reacts with that "tone" in his voice-- usually anger or frustration.
I feel your frustration. We have been in a similar place to the point where we just stopped communicating. He is finally just recently realizing that communicating isn't as hard as he thought, that it prevents a lot of problems in the first place, and that it's opening up a world that he didn't know existed.
But I tried for years to get him to understand that... and never succeeded. He finally got there on his own, but I'm not really sure what was the turning point for him. Maybe I'll ask and see... but whatever it was it was inside him, and not something I said to convince him.