Murdock1973 just a bit of unsolicited advice for the future. Please dont take this as any sort of lecture or criticism, its offered in a well meaning manner.
With respect to arguing or "debating" with other coaches, supporters or adults around children and even young adults the best thing you can do is not argue. Take anything like these types of disputes via alternative channels.
A couple of reasons. Firstly despite the fact your team may in fact support you often kids feel embarrassed when adults have heated arguments. Its their game, their playing time and when we get into (often well intentioned) defending of our players we end up showing them a side that may over time lessen your standing among the players. In numerous studies around the world over a number of sports its been found that kids find adults being too vocal, arguing or expressing annoyance loudly is embarrassing and off putting for players. Your players wont ever tell you this.
I have no doubt the other coach you had to deal with was an arse. The better approach to the whole issue would be to have a quiet discussion with your players at traing a few days later where you lead the discussion without expressing your own opinion and guide the players to conclusions with questions that help them find the best answers. You will end up earning a lot of respect from your players whilst helping them grow and mature.
Its very difficult to walk away from jerk coaches because often we are trying to stand up for whats right. But long term using channels away from the playing pitch and your players is the best approach. Easy to say but it is hard to do. All the best.
p.s I learned all of the above the hard way.