It could be because they are struggling with a delusion that puts you in a very bad light in their mind. People are out to get them, and you’re in on it. Maybe you personally are out to harm them in some way. Maybe people are out to get them, and you’re in denial about it, and thus making things worse. (As possible examples of how the delusion might involve you.) Hostility is a normal reaction if you believe that someone is trying to harm you, and severe anger is a normal reaction if you believe someone is being willfully ignorant and it’s making your situation worse.
Sometimes it could be because of very high levels of stress, which can make someone very agitated in general. So if you were to do or say something that was only slightly annoying, during a very high stress state, the person could feel extremely agitated by it instead. In some cases stress can also come in the form of trying to cope with having a mental illness in general, feelings of dependency, indignity, vulnerability, etc can all make someone feel very stressed and angry, in addition to sad and so on.
In some cases, it’s because well-meaning loved ones take on very condescending attitudes, talking to the mentally ill adult as though they are stupid, a child, or too “crazy” to have their thoughts and feelings count for anything. This will make almost anyone piping mad, to be treated that way, but when compounded by the stress of mental illness, talk about furious.
All things to consider.