Wow the lack of knowledge about asexuality here is staggering.
It exists on a spectrum, and yes asexual people can have feelings for people, but there's no sexual side to it. Some are sex repulsed. Some are demisexual and only feel sexual urges once love has been established. It sounds like he is sex repulsed.
I feel sorry for him actually, you're clearly good friends and now he's going to have to make a choice. Is his partner clingy in the same way when it's other men he's talking to, or only women?
Here's some terminology for the clueless folks:
Aromantic - someone who doesn't experience romantic feelings. Is sometimes present in ace people too. Some allosexuals are Aromantic which is why they might be comfortable with casual sex or FWB arrangements. Can he shortened as "aro."
Allosexual - someone who experiences sexual urges. Can be shortened to "allo."
Asexual - someone who doesn't experience sexual feelings, or only under certain circumstances. Can be seen alongside someone who is asexual. Can be shortened as "ace."
Demisexual: someone who only experiences sexual urges once love is established. Can be shortened as "demi."
Asexual people experience intimacy in different ways. For example, when they share personal things about themselves, or open up to you about things, this can be classed as intimacy for an asexual person. An ace friend of mine told me that when she and I talk about her worries and vulnerabilities, how important the things in her life are that make her happy, THAT is the intimacy that she chooses to share. The trust she shows me by sharing things. Most people simply consider this normal friendship, but we still apparently can't handle people of opposing genders being friends, which is so utterly ridiculous.
Your friend and you are clearly very close. The fact that he shares things with you that he might not with her, will probably upset her because it's an emotional level of intimacy that he might not share with her.
She is clearly jealous, and allosexuals can't really grasp that others don't feel anything sexually, so the very moment an ace partner seems close with someone of an opposing gender, it will likely make them feel inadequate.