In addition to what others here have said, there's plenty of forms of trauma that have nothing to do with abuse: harrowing situations, disease, loss of loved ones, and mental illness all come to mind.
You mentioned a character who is worried about being attractive or else everyone they love will leave them? Maybe they have some minor disfigurement or scar from childhood, and there was one moment in middle school where some kids pointed and laughed, so ever since they've developed a complex over it. Maybe it's a self-inflicted obsession due to having an older sibling or parent they looked up to and wanted to emulate that worked as a model or fashion designer or something. It doesn't need to be an abuser who puts toxic ideas into the victim's head: people are plenty capable of coming up with those all on their own for a bajillion different reasons.
And all that is just ideas I came up with off the top of my head if you want or need to explain where someone's personality traits came from. Some people are just obsessed with looks, and would leave a partner who wasn't attractive enough to them, so they assume the same of everyone else. Sometimes it's just a 'how you are' thing that isn't necessarily linked to your past, and oftentimes even when it is, you as the storyteller don't have the time or attention to devote to explaining every little detail of every single person's life in order to justify them being every single little way they are.
If it comes up and is relevant, then yes, you can have explanations, sometimes even justifications, for it, but most people don't know every single detail of every little moment that made every single one of their friends have every single personality trait they have, so why would an audience expect stories to have that amount of information?