1) He was taking cheap shots at other players. Whether he is a coach or a player, this is unsportsmanlike and dangerous. Now some may counter that the sport is inherently dangerous, but what he did was not part of the sport that people voluntarily choose to be put in danger for.
2) He is an adult striking children (or young adults if you want to be nice to them). This could easily be a criminal offense here.
3) He is a non-player attacking players.
The coach had no right to punch the opposing player. As a coach he was put in a roll of leadership and should be reprimanded. Aside from physical outbursts, there should have been another way to express his anger, a more professional way. Some sort of punishment needs to happen to make an example of unacceptable behavior.
A college football coach is often an influence for young players who are still looking for role models as young men coming of age. Many of these young men grew up in households without fathers, so sports coaches become like fathers to them. To have a coach set this type of poor example for young players is inexcusable.
I haven't read anywhere that he punched the opposing team's player but I did see that he got ejected for a helmet to helmet hit. And yes, he should have been ejected for that play. it is dangerous not only to the other player but also for himself. If we want to see football continue to be a sport than this kind of stuff needs to end
These days, even the smallest scuffle in professional or college sports can raise a big stink and often a fine and/or punishment from the respective organization. But I think we forget what it's like to actually be in a competition like that. Tempers flare, and things happen. Players shouldn't be penalized because our society has been so thoroughly sanitized of overt displays of violence, even as violence persists in pockets throughout the world, including our own society.