All my 20s and 30s I was desperately searching for a couple and socialization the way you describe.
If you ask for a radical solution, and you're from English-speaking country, my radical suggestion is: go teach English in country like Brazil or Russia, Ukraine, etc, but make sure you stay outside of the capitals, where expats are rare enough. I know some guys who did this, they have social life, are rather important people, and have no reason to come home to be the average Joe.
If that's not an option, like it wasn't for me, manage the probabilities. All hobby groups are places where you have a chance to get some social life/couple. But they differ. Invest less time in those with awkward people, but don't abandon completely -- sometimes friends from there will invite you to other, more interesting social groups.
Eco-, new-urbanism or political activist groups are much better than dance groups, because people go to dance exactly to find a couple, whereas any form of activism filters those out and the share of "normal" people is much higher. (Of course, their age and marital status may vary, so choose appropriately.)
Where you live also matters. A metropolis is very un-social, interactions are awkward, and you must be highly active to just stay in contact with some people. A small town has much more social cohesion, but may make you passive in dating. Something in the middle is better.
Living in suburbia is antisocial, it's better to live in walking distance from places to socialize in a walkable city.
Since you're still looking for a couple, it's better to live near a university where the share of young people is higher. Also, write down when you had dates, or was approached, and what social activities you had then -- it can give insights.
P.S. Therapy works only as painkiller. After couple of meetings therapists open up their stone-age beliefs: NLP, positive thinking, hypnosis, homeopathy.