Many sources talk about how sustained eye contact is an aggressive gesture for housecats, and that’s true as far as it goes, but I think there’s a widespread misunderstanding about what “aggressive” means in this context.
When it comes to animal behaviour, an aggressive gesture doesn’t necessarily mean “I want to fight you” - it just means “I am trying to provoke a response from you”. The expected response might be violent, or it might not be.
The upshot is that if your cat is staring you steadily in the eye, it doesn’t necessarily mean “fight me”. In all likelihood, mostly it means “feed me”.
(Other possibilities include “follow me”, “play with me”, and “something is wrong, but I’m not going to tell you what - you have to guess“.)