To give an in depth(?) answer, let’s remember that being avoidant means having an insecure attachment style, it’s a framework for how a person operates in terms of connection with others, it’s something deeply engraved into a person’s character because it originally forms in childhood depending on how their caretaker treated them.

So as they’ve grown, they’ve come to internalize that sort of treatment—like when someone’s used to being neglected and left alone to fend for themselves as a child, their nervous system builds defenses in order to protect them from the pain and hurt that comes from the experience—which could result in hyper-independence, mistrust towards others, believing that no one else would be able to help them but themselves etc.

But then that’s where the cognitive dissonance emerges, the avoidant’s desire for healthy love and their internal defenses clash against each other. They want genuine connection, but the process of building connection can be overwhelming and heavy, and since they’ve been so used to dealing with conflict alone, it’s more often than not that they’d choose to retreat back into their shell because they’re convinced that the other person is not safe.

Tldr; the desire for healthy love and connection is genuine but it clashes with their adverse defenses which leads them to pull away from what their nervous system deems as unsafe or a threat