Yeah I agree with OFL. I have a male and female living in a divided tank who I let have supervised visits when I'm cleaning it as I have to remove the divider to reach the back.
They are perfectly fine when supervised as I quash any aggression by either fish, and usually the female is assertive enough to chase the male off.
However, the other day they got in together by themselves and the female ended up with her whole tail shredded. Obviously the dynamics had changed when no one was there to separate them and the female had come out the loser.
Unless you want to breed there is no real reason to try keeping a pair together. It's only going to be a stressor for both fish, and is either going to end in an accidental spawn or severe injury/death.
It's really hard to pinpoint subtle aggression in bettas. Brushing up against her and seeking her out makes me think the male is being aggressive. The female has probably avoided attack by being submissive and not retaliating.
Some of my male wilds only have to look at another male, and the other male will immediately stress-stripe. It's all very psychological warfare, and this can sometimes be as stressful as physical attacks.
Stress in bettas, and fish in general can lead to a compromised immune system, which is why you often see outbreaks of columnaris and other diseases in sorority tanks as these are a high-stress environment.
If it was my fish I would separate them ASAP. Not worth the risk.