Some fish may gorge if overfed (I know my platys would)- but then it will pass right through them and end up as waste fouling the tank. And some food will not be eaten if you feed too much- so will also foul your tank. In other words, ammonia poisoning is the most serious danger of overfeeding, and it can happen quickly. Even mild ammonia poisoning will lay them open to disease. Constipated fish is another risk.
Then again, if you underfeed, they may miss out on the nutrients they need to stay healthy. Though it is fine to leave fish without feeding for a week or so once in a while, persistent underfeeding will leave them less strong and able to ward off infection. It is sometimes stated that fish are always underfed in nature, and that this is somehow good for them, but actually what happens in nature if there is a more than a temporary blip in supplies is that population numbers adjust themselves, i.e. fish die. Which is not what we want in our tanks.
So what is overfeeding and what is underfeeding? Tricky one, as it depends entirely on what kind of fish you keep. I hate the common instructions of "as much as you can pinch between thumb and forefinger", as they totally ignore the fact that not all people keep the same fish or the same number of fish- or indeed have the same size thumb and forefinger! I can pinch an awful lot between my thumb and forefinger, probably enough to poison a whole fish shop. A better way is "as much as they can eat in 2 minutes"- though this does not work for veggies, as they take longer to chew.
When I got my fish, I measured out the flakes for them for the first few weeks until my eyes knew what was a reasonable amount. I worked on the assumption that 2-3 flakes a day, divided into twice daily feeds, would be about right for smallish fish like platies and guppies, and when I substitute (jellied) "live food" or veggies I aim for similar amounts. My 4 corys share one catfish tablet a day, but also get jellied "live food". For small tetras, I would feed maybe 1-2 flakes each a day.