Asexuality can be about more than just sexual attraction and lack thereof. There have historically been multiple avenues to asexuality.
First of all: of course, you don't have to identify as ace if you're sex-repulsed/sex-averse, but feel like your attraction has something else going on that's important to you. And of course, you can identify as ace if you're sex-favorable, but feel like your lack or near-lack of attraction is important to you too. Nothing I am about to say negates those things.
However, for some people, sex aversion/repulsion is the most important factor in falling under the mantle of asexuality. The most important factor in resonating with the language of asexuality, finding a home in the asexual community, and considering asexuality both an identity they can take pride in, and use to communicate their experiences.
As useful as it can be to describe and discuss sexual attraction, said sexual attraction is ultimately a social construct that may be impossible to parse, uncomfortable to parse, inapplicable, and/or irrelevant to many on the asexual spectrum. Many of us active in the asexual community are familiar, either firsthand or secondhand, with how slippery the concept of sexual attraction can be â the turtles in ponds metaphor, the search for something you're not sure you even know the shape of. What's the boundary between attraction and non-attraction, between sexual and sensual and aesthetic?
Really, should something so slippery and confusing be the only metric we're allowed to define ourselves by? I argue it can be useful for many, but should never be a requirement â and personally, it's not how I define myself. I identify as asexual in part because the question of "Do you experience sexual attraction?" is fundamentally impossible for me to answer. An intractable problem, which I reject the need to answer or solve in order to know myself as a person.
Moreover, asexuality has a long history, serving as a useful term and community to ace-specs with a wide variety of experiences with attraction, desire, and action. While the "Non-Libidoists" of the early 2000's were by no means correct that a lack of interest in sex/masturbation should the only avenue to an asexual identity, they highlight that aversion and indifference to sex have been many people's reason to find a home in asexuality, throughout much of that term's usage.
Multiple avenues to asexuality are possible, and that goes both ways. Asexuals who have or want to have sex need to be welcomed and cherished, but positing that "little to no sexual attraction" is the only valid definition of asexuality is an overcorrection â and an alienating, exclusory overcorrection at that.