@elefantine97
There isn't really a simple answer to that, because asexuality is a spectrum in itself, and everyone on that spectrum experiences asexuality differently. Some ace people are sex-repulsed, where physical intimacy is undesirable at best and traumatic at worst. Other ace people, as you point out, do have sex drives, and even engage in physical intimacy. One isn't any more or less ace than another, because ace is an umbrella term covering a wide spectrum of distinct orientations.
For me, the metaphor I like to go with is coffee. Some folks drink coffee, some people don't. Some folks love it, some folks hate it. Some will drink it of offered, but won't go seeking it out. Other people don't drink it, but they like the smell. That's where I land.
In this case, she certainly could simply be insecure. I'm reading asexuality into this because many of the hallmarks of "closeted asexual" are there (dating not out of a desire for companionship but because you feel like you're supposed to, being miserable while in relationships even when you like your partner, feeling broken for not feeling attraction, etc.), and also because I'm doing some wishful thinking. Seeing asexuality represented in art means a lot to me, and I can literally count the number of times it's happened on one hand. It'd be nice, yaknow?