He wants to do counseling, he swears he doesn’t want to leave me, that he loves me and is very attracted to me but my "rejection" of him for so long made him feel depressed and to loose his confidence, that’s why he went looking for it somewhere else.
Blame-shifting is how you know that the WS isn't really sorry. Cheaters typically need to rationalize why it's okay to betray their partners. They have to fix it in their own minds so that it's their spouse's fault and not their own. That way, they can continue believing that they're simply splendid people and not creepy sneaks. I doubt very much that your WH was made to "feel depressed and to lose his confidence". Instead, he was probably pissy that he wasn't the center of your attention and that his sexual entertainment wasn't your priority. The proof in the pudding is that, yeah, he'd have probably had a lot more sex if he had put that effort into you rather than strangers on the internet. You see how the blame-shift is exposed, right. It's in the payoff.
It's an old Dr. Philism, but no less true for the folksy delivery, "what's the payoff?" It's the payoff which drives the behavior, and your WH is trying to convince you that his behavior was predicated on yours. IOW, YOU control his integrity, his morality, his actions. You must be a goddess, right? An all powerful being who bends him to her will with a snap of her fingers. 
Or... he's blaming you for behavior that HE CHOSE based on what he gets out of it.
Cheaters rarely cheat for the extra sex. If it's about an orgasm, they can do that for themselves with practically no time or resources put into it. It's about the experience. It's about the way a new conquest makes them feel. It's about the validation they get from proving to themselves that they've still "got it". The cheater would have us believe that we somehow MAKE them throw away their values and do something completely out of character because we've driven them to unaccountable levels of desperation. They'd have us believe that the relationship is the problem, that WE are the problem, but that's just not the truth. The truth is that cheating happens in otherwise good marriages where there's lots of sex, and the truth is that we are NOT gods who can control another person's behavior.
To cross a boundary that we care about, we have to make a choice. It doesn't just happen. People protect what they value, and if a person VALUES honesty, fidelity, integrity, they have boundaries around those things which they won't cross. So, this is a guy who demonstrably LACKS those boundaries, who is attempting to convince you that you are the arbiter of HIS morality and that his good behavior is predicated upon yours. You see how he's abdicated responsibility for himself and made YOU the parent, right?
The payoff for the behavior is the feel-good dopamine cocktail he gets when his phone pings. Sure, he likes your kibbles. If you were following him around like a groupie and you were throwing your panties at him like it was 1970 and he was Tom Jones, yeah.. he'd get a big kick out of that. But your kibbles are known kibbles. They're not CONQUEST kibbles. The payoff is NOT the same. The drive to attract strange is about conquest. Validation of one's attractiveness and sexual prowess is the payoff.
The guy is bullshitting you. Maybe he's sincere about it because he's not self-actualized enough to know what his real motivations are, but it's bullshit nonetheless. Worse, this kind of behavior tends to escalate when it's allowed to fester. It has to be remediated, otherwise, it's quite likely to repeat and worsen. I'm going to reprint an old post for you rather than type it all up again, but the bottom line is that this is NOT your fault. Your WH has a problem that he needs to fix. You can't fix it for him. You're not actually a god.
My own WH went on a Craigslist binge seven years ago, multiple partners, various degrees of emotional attachment. He even thought he was in love at one point. But ten years before that, I'd caught him out in some online shenanigans, porn, cybersexing, emotional affair, etc. In fact, I caught him out only two weeks before a planned meet-up. I'd already seen an attorney before I confronted him and I was bent on divorce, but he pretty much cried his way out of it and I settled on MC. As you might have guessed already, we too were bamboozled with the "unmet needs" model of therapy, which sounds so reasonable. I upped my wife game, and did my best pick-me polka, but within a couple of years, he was right back at it behind my back. By the time we reached the ten year mark, he had screwed up his nerve to go live and in person on Craigslist.
Of course, I was pretty shocked as you might imagine. I thought we were good. I thought his "needs" were met. Damned if I hadn't been turning myself inside out for a decade to make sure, right? The more I thought about it, the more I revisited what I knew about the "unmet needs model", the less it made sense. I was doing everything right and he still CHOSE to cheat.
Here's the fly in the "unmet needs" ointment...
Healthy ADULTS don't need to be validated. They validate internally. Healthy adults are self-fruitful in the matter of contentment and life satisfaction, and when things come up which make them unhappy, they address the cause and solve the problem. OTOH, the vast majority of cheaters cheat because they're seeking external validation. They are NOT emotionally healthy. They can't do it on their own. They've got a hole inside them and no amount of external validation will fill it. Certainly, the old and familiar validation of a spouse doesn't get the job done. Our "kibbles" are stale and boring. They don't create enough adrenaline anymore to make the cheater feel special. It's like getting an "atta boy" from your mom, right?
This is old pop-psy which is still being taught in schools and still selling books. But it's bullshit. NOTHING you can do (or fail to do) can MAKE another person throw away their core values and do something that's in this kind of opposition to good character. If you're a person who BELIEVES in fidelity, who VALUES fidelity, you don't cheat. End of story. Because when we truly value something we protect it. The cheater has a "but..." in his values system. ie. "I believe in fidelity, but... not if my needs aren't being met." For people like you and me, we have a "so..." in our values system. ie. "I believe in fidelity, so... I don't put myself in risky situations with the opposite sex." This is the BOUNDARY we create organically. We don't sit around planning it out. It just happens, because it's innate to our character to protect what we value. The cheater doesn't have those boundaries because he doesn't really honor his values. He only claims to.
I'm not saying that your marriage is over or that your WH can't change. What I am saying though is that this "unmet needs" model is NOT going to challenge him to clean up his flawed character. In fact, it allows him to offload responsibility onto the marriage and onto YOU. It's not your job to MAKE him feel (fill-in-the-blank-here). It never was. It's his job to manage his feelings. You could have been doing everything exactly perfect for the entire length of your marriage, and he would still have cheated... because there's NOTHING in his character stopping him and he has no coping mechanism to fall back on when he feels unvalidated, inadequate, unappreciated, etc.
It's HIS job to see that his "needs" get met. Sometimes that might mean negotiating with you, say if it's about sex or about the division of labor in your home, etc. But sometimes, it might mean that what he sees as a "need" is unhealthy in an adult, like external validation through attention and flattery.
MC's are there to treat the marriage. The marriage is the client. So, of course they're going to talk about communications, resentments and expectations. The MC doesn't want to alienate anyone, so s/he's looking to find balance on both sides. But marriages don't cheat. People do. The only way your WH is going to make a change that safeguards against further perfidy is by correcting his need for external validation and becoming an emotionally healthy adult whose deeds are as good as his word. No excuses, just honoring the things he claims to value. For that, I would recommend IC (individual counseling) with a therapist who is well-versed in adultery.
The last thing any newly-minted BS needs is to walk into an MC's office, believing that they've come to safe harbor, and being handed a copy of The Five Love Languages or some other "unmet needs" gobbledygook. It would be really nice if we actually did have the power to control our mate by giving them "acts of service" or "words of affirmation", but sadly, we aren't gods who can stop a cheater from seeking out his/her choice of adrenaline rush and new kibbles. Although, this kind of pop-psy suggests that their behavior is somehow our responsibility. The more you dig into this ridiculous line of thought, the more absurd it becomes.
Anyway... sorry for the lengthy post. Nothing fries my ass more than seeing new BS's being sold this bill of goods.
