For those of us that have been in relationships, we're better able to weigh the need for companionship versus the costs of said companionship. Being wanted by someone that isn't good for you isn't a net positive gain. And the energy it takes to sort through humanity to find someone that is good for you is also a cost to factor in.
If I was to weigh it objectively I'd say they were a net gain for me - I've learnt more and shared something with people I've been in relationships with than anything else from 'normal' friends or family. More than that, whilst I pride myself on being a rigorously logical person, I think it's shallow to put relationships down to an objective cost-benefit analysis. There's a reason that most of the human race (and the reason everyone is here) has been in relationships of some sort, and I think it's because a truly great relationship goes above and beyond just 'does the fun outweigh the risk'
Whilst I don't think being completely alone is healthy, it's not that it can't work; there's always the small proportion that are completely different to everyone else and that's fine. However, I have to agree with the Lord that I think there's some self-delusion when a lot of people say they want to be alone - from what I've read here (and a lot of other people) they're scared/hate the idea of rejection to the point where they don't want to risk it, rather than that they actually truly don't want to be close to someone. All I can say is that from my experience, it's worth it in the long run.
That being said, a 'traditional' relationship may very well not work for you. I know a lot of people in all sorts of 'alternative' relationships. One of my friends classes themselves as completely asexual, however they have a very loving relationship with someone without any sexual component for instance. It may be you need to think about what sort of 'closeness' you want and how you think you can get it as it may be radically different to the 'norm'.
If you are that type of person though (anxious and depressed) then you can't exactly be honest about it when you're trying to meet people. It's a real turn off. You have to either endure being single until you're ready to meet people or suppress your symptoms and put on a face, neither of which are particularly healthy.
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As someone who has never had a relationship, it's completely soul-crushing. It's wrecked my self-esteem and the longer I go without the more I end up obsessing about it.
If you're also depressed then it feeds right into that too. The misery and hopelessness of it becomes a part of who you are and ultimately the centre of your existence.
I'm genuinely sorry to hear that - I really am. I think the core is not to rush it - whilst I do think it's an important thing, it's not something that has a time limit on it so you don't need to worry about it happening right now. I know a lot of people who haven't found someone serious until late 40s and that worked for them.
As with the OP, you may need to go wider to find the 'right' person for you - if you have social anxiety, meet someone you can chat with for ages online with first and then meet doing something you're comfortable with. I know one guy who was terrified of dating but he was a mini golf pro - he always used to take them there, as he had something he could concentrate on no matter how it was going. He even used to go for a test run if they changed the track.
It's also fine to be clear about your situation - you don't need to reel off your symptoms to them, just say 'So, I find it hard to meet new people - would you mind if we chatted for a while before we moved it further?'. Again, couple this with working on yourself religiously - gym, learn a skill (to the point of mastery) and take care of yourself as best you can - even if gym/whatever isn't you, try it for 6 months and get back to me.
Not qualified at all, but if anyone's struggling and needs a chat/vent, I'm a PM away.