A display, not the start of a fight
Fin twitching — a rapid flutter or shiver run through the fins while the angelfish holds its position facing another fish — is body language, and in cichlids it is low-level signalling. The message is some version of: I am here, I am larger than I look, and this spot is spoken for. The other fish reads it, answers with a smaller display of its own or drifts away, and the whole exchange ends without contact. That is precisely the point of the twitch. Angelfish settle most of their disagreements with theatre, and a fish that can win an argument by shivering its fins has no need to start a chase it might have to finish.
What the twitch is saying, and to whom
Context tells you which message is being sent. Aimed at a tank mate of similar size that has wandered close, the flutter is a rivalry display — a warning shot fired early so nobody has to escalate. Aimed steadily at one particular smaller fish, it is a boundary notice, and worth watching in case the notices start arriving with charges attached. Aimed at another angelfish while the two swim parallel, bodies angled, colours deepened and fins held stiffly out, the same shiver is courtship: pairs test each other with display for days before they ever clean a leaf together. The fish itself, its posture and its audience change the meaning of identical-looking movements, which is why the twitch alone never tells the whole story.
Twitching that is not a display at all
There is one look-alike that matters. A fish irritated by its water or its own skin also flicks and shivers its fins — but that fish rubs. It flashes its side against gravel, wood or glass, scraping at an itch it cannot reach, and the fin movement is part of the wriggle rather than a signal aimed at anyone. Display is directed at another fish and stops when the audience leaves; irritation follows the fish around the tank, audience or not. Twitching that arrives with rubbing, with fins clamped tight between shivers, with white spots, rapid breathing or a fish hiding instead of posturing, belongs in a different conversation: test the water first, then look closely at the skin and gills.
Living with a fish that talks with its fins
If the twitching stays theatre, there is nothing to fix. A hierarchy settled by display is a peaceful tank working as designed, and your job is simply to keep the stage workable: plants or wood positioned so the fish that loses an argument can leave the conversation and break the line of sight, and enough room that a warning does not have to become a pursuit. Keep a light note of the pattern — the same rival every day, a display that only follows feeding, a flutter that is slowly growing charges at the end of it. Escalation over weeks suggests the tank's space or stocking is tightening around this fish, and that is a layout question, not a behaviour fault. If a flutter starts arriving with charges attached, or the same rival is targeted day after day, put a follow-up question to KinsLe's Kimmy; she answers using the KinsLe Answers library, so the display in front of you can be read against what fin-twitching usually means.