A sub for a team I reffed on Sunday wouldn’t shut up and was on a yellow. After shouting “did you not see that one ref” I walked over and said he could either take the whistle and see how he likes it or keep quiet for the rest of the game before he walks.
And when he hold out his hand out for the whistle and says, "Great, I can sure as heck do better than you've been doing."?
Sometimes the cute comebacks work, but they can back fire.
Coach says to me we not playing offsides sarcastically and In a rude manner by walking on the pitch to which I respond yes we are and explain my reason for the offside decision. To which he responds “calm down I was only asking a question” so it’s ok for him to speak to me rudely but the second I raise my voice it’s wrong. Treat others how you expect to be treated
I'd suggest you only give answers to actual questions. The knucklehead didn't ask a question, he was baiting you and had no interest in an explanation. (You also say he came onto the pitch to do it--entering the pitch to confront an official is a send off offense for a coach.) IMO this is one you need to kill right away, not enter into a discussion. You don't say how far onto the pitch he comes, which affect options. If it's just a step, easy to overlook, and just shut it down--"That's enough coach, knock it off." If he comes well onto the pitch, then that's what your red card is for. Somewhere in the middle there might be a caution option as well.
If you
are going to have a conversation (again, I wouldn't in this context), instead of going over and starting to explain, consider going over and asking "tell me what you saw" and let him talk. Listen and wait till he runs out of steam.
Then say something like, "Thanks for sharing that. Here's what I saw--while your left and center backs were up, your right back was a yard further back when the ball was kicked, keeping 24 onside." If he interrupts, while you are talking, it is then easy to say "Coach, I let you talk, now it's your turn to let me talk."
Remember that you never need to win an argument with a coach or player. You already won by having the whistle and control of the decision. So you don't need to raise your voice--if you feel you've reached the point where you would raise your voice, it's a good sign the coach has gone too far and it is time to pull out the yellow card--very calmly. As the referee, we always want to be the most calm person on the pitch.