I think of what you, possum, and childofchaos are describing as isolation rather than loneliness.
Perhaps that's just a semantic difference.

I am unable to fully connect with people, and I suspect no one can with anyone, and that feels bad, but it doesn't seem to be exactly what people mean when they say they are lonely. For example, most people try to 'cure loneliness' by meeting people - but if the issue is that one cannot form connections with people then this would be a pointless attempt at a solution.

So, I seek company not to end the bad feeling of isolation, which cannot be ended, but simply to alleviate boredom, which could also equally be ended by finding solo activities.

Does that make sense?