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Has your boyfriend read "The Five Love Languages?" If not, he should read it. If he has, then he has no excuse for asserting that a need for words of affirmation is some kind of a pathology. What I see is a pathology on his part that he's trying to re-direct onto you because he doesn't want to deal with it himself.
If your counselor can't get him to accept the "words of affirmation" idea, then you either need a different counselor, or you need to seriously think about whether this is a relationship that's good for you. It's great to love someone, but that doesn't mean you're obligated to follow them down a whirlpool they're determined to plumb. He has a pathology that he's not willing to talk about, and certainly not willing to work on. Meanwhile, it's eating away at your psyche to be treated this way.
People who love each other develop an appreciation for each other's love languages. He isn't even trying to develop and appreciation for your love language. That's not a good sign. It says to me that he wants to get his way even if he's continuing to hurt you in the process. That doesn't show love to you; it shows love to himself.
I'm afraid you can only get to the bottom of this if he agrees to open up, and that's his decision. Trying another counselor is about the *only* option I can think of for you, shy of letting the relationship with him go.
I'm sorry he's depressed and dealing with a lot in his job and life but that *doesn't* make it okay for him to refuse a very simple, reasonable, easy-to-do request on your part. I'd give him a fixed amount of time to start showing some verbal improvement, mark in on the calendar and inform him about it. If the date comes and goes and he still refuses to express anything good he sees in you, I would regretfully cut the ties with him.
Of course, there's always the option of just letting him do this to you for the rest of your life. But does that really sound like a good idea? It's all well and good to take care of him, but you need to take care of you too.
Sorry you find yourself in this pickle. Hope some changes for the better are on the horizon.
Love means never having to say, "Put down that meat cleaver!"