Well love, my own position is slightly different.
I have a real problem with genophobia, that is fear of s/x and with touch. For this reason, I've never had a relationship, despite having a desire for one which has sometimes become so strong it's been physically painfull, yet because I'm male, because I'm expected to make the first move, and because I can't perceive those mysterious signals that are supposed to initiate these things, it's never happened.
For this, for my own protection I've made a resolution to cut out that desire in myself. It was my attempt to do something about a relationship that landed me in recovery in the first place, and from where I'm standing, it's brought me nothing but a lot of pain, so it has to go. I don't always succeed at removing this desire from myself, but the more I practice, the easier it is, especially when I am devoting my life to something more fulfilling, such as music or creativity.
This is a slightly different matter to what I believe hd and lanser mentioned, which is the matter of intraversion, that is, relaxing by spending a lot of time alone, away from anybody, which is not the same thing, sinse there are plenty of people who are in perfectly normal relationships who are natural intraverts and relax by being alone (my mum is one, and so am I), though for survivers solitude, like any other addiction can go too far (something I've struggled with myself).
this is quite a different thing though, sinse it's still possible for an intravert to have an intimate, loving and fulfilling relationship with someone else, ---- indeed many of the successfull couples I know are one intravert and one extravert, it just means that where the extravert relaxes by talking to someone else, spending time with other people (often strangers), the intravert relaxes by spending time alone by themselves.
Both can bare! the other situation, the extravert isn't going to freak out if they are alone for a while, and many intraverts (including myself), develope sufficiently good social skills to cope in situations with others, but essentially this is more a matter of ease, comfort and relaxation than a desire for a relationship, though as recovery destorts everything elseI'd say it's quite possible for an intraverts' desire for aloneness to become too much or be destorted into isolation.
Such would be my thoughts anyway.