How does one go about politely firing a chess coach?

Firings happen all the time...........my son needs a break from you.   he has not been gaining knowledge / ratings and we want to explore another direction for him.   ( that is not bad to say )  Perhaps he will not use a tutor for awhile.   He may simply read chess books and play in clubs for awhile.......etc.    Thank you for getting him to his current level.   ( what more could you say ?)

If your son isn't getting a benefit, just tell the coach you are taking a break from coaching or exploring different training options.

However, you can't necessarily blame the coach for rating stagnation. A student has to do the work as well and it may take a while for some of the material to really help and be reflected in the rating. Maybe that stagnation is one of the reasons for the suggestion of a repertoire change.

If the coach is being hired by a parent who:

1. believes 50/hr is daylight robbery
2. has "designed an opening repetoire" for their child
3. claiming the KID is unsound

I am sure he won't be crushed to lose this teaching gig.

Just say "I've decided to go in another direction, thanks for everything you've done." This isn't difficult.

1. £50 an hour is day light robbery for a lowly FM. What other job do you know pays so much?

2. He is undermining my role as a Father by not consulting me before making these decisions.

3. The KID is unsound. Kasparov stopped playing it for a very good reason.

Many sound openings are very drawish. There are many notorious book draw opening from move 15, move 20 , move 25 etc.

KID may have slightly worse chance of losing than other openings but it is not important among lower rated people < 2300-2400.

Learning KID is very rich in theory with pawn structures, pawn breaks etc.

Paleeeez! 

Okay, so every player has ebbs and flows and hits certain rating plateaus. sometimes they get stuck there for awhile, other times they quickly move on to a higher level. But at some point, every player is going to hit some level where it begins to get very difficult to go any higher. This is not a sign that the coach is ineffective or not doing his job - it is just a fact of life.

With regards to your comment on changing your sons repertoire (that YOU made for him) - if you are that great, why are you not coaching him? Maybe the coach thinks that your son is playing his openings too much by rote, and is not really thinking. He may be wanting to mix it up a little to expose him to new concepts and ideas and get him out of a rut. Taking a look at your ratings,, I am not sure why you are attacking a FM as his rating must be hundreds of points above your own.

What repertoire did you outline for your son? 

Finally, the KID is unsound???? Really? I think Tal, Fischer, Kasparov and many other really great players would have a field day with you on that point.  

P.S. Kasparov stopped playing it as he got older not because it was unsound, he wanted to play something  a little less sharp as most aging players tend to do. During his prime years, including numerous World Championship matches, he constantly played the KID. Risking a WCC crown by playing unsound openings? - I think not. 

Knowing nothing about the coach in question, an independent business person has to cover all cost associated with being the employee and employer and make enough to weather downturns in student levels. If that is their only income, that doesn't sound that bad; more than I would want to pay for a coach, but for some it may be worth it.

imo, its the student's fault if they plateau. I take it your son is somewhere around 1500 on chess.com? If so, there's no reason an FM couldn't provide adequate coaching (unless they're an awful coach). Most people, with enough time and dedication, don't plateau at 1500. Especially if they are young.

My coach helps me change my repertoire all the time, and I find the openings he teach me suit my playing style WAY better. For example, i used to play the Exchange variation against the French, with sub-optimal results. My new coach told me to play the Tarrasch, and we went over some lines in class together. The result? I got a winning position (>+3) against a 2200+ rated WIM after the first 30 or so moves. Often, coaches recommend certain openings based on their student's playing style.

Also, I don't think outlining a repertoire for your son from the get-go is a good idea ...especially if you aren't willing to change it. I remember when I started (In Aug 2018), I was reviewing some top games in my free time and stumbled on the games from the 2018 Candidates tournament. Fabiano Caruana, the eventual winner, played the Petroff with great success, so I, naturally, wanted to learn the Petroff. I compiled a whole list of cool openings I saw top GMs play, and tried to learn them. And guess how many of them I play now? Zero. They didn't suit my style at all, and I just couldn't get a decent middlegame position. It was worth learning new openings to get where I am today. In fact, I'm in the process of revising most of the openings I play again.

Finally, the KID isn't bad. I won a game just a few months ago at World Youth with it.

I didn't know coaches only got paid £50....must be the modern day starving artist

Only a 1400 would call the KID unsound 💀

I dont play that variation of KID

1. Would seem a bit high for an NM but sounds normal for an FM (maybe on the low side depending on whether or not travel time is included). It is much easier to get a cheaper FM to give lessons than it is to get an FM to give effective lessons (the FM needs to know how to teach, not just how to play, and an FM that is a good teacher stands a good chance to be better for a sub-2000 player than a GM that is not a particularly good teacher). Many US parents have a tendency to want their kids to gain 500 rating points per half-year indefinitely (not realizing that it is a LOT harder to go from 1400 to 1900 than it was to go from 400 to 900). A parent that wants a steady rate of increase (unsustainable over the long run) can end up stressing out a kid and driving the kid away from wanting to do anything with chess.

2. If you were planning on controlling the training then there was no reason to hire anybody. Chess teachers in the US are used to either working with students to find the openings most suited with them, or limiting themselves to what the parents want the kids to play and ending up with a reputation for being ineffectual. The stagnation may be due to resistance to the idea of changing the openings.

3. Seems like a clueless comment. I rode the KID to more than 2100 (figure 2000+ for the FIDE equivalent) before getting married, having a son and not having time to do the studying that I didn't have any inclination for anyway (I play chess for fun and if it becomes work then it is no longer fun).

Just tell them that you're no longer interested in their services.

Troll and gaslight him until he goes insane and quits coaching forever

If he's upped his prices, he's goven you an excuse on a platter.

However, I agree with everything said above about your reasons for firing him not being very good. If you can't afford his fee, that's fine, but it's not in itself unreasonable. If you have concerns about your son's progress then why not discuss that with the coach and see if you can work together to address it.

Adjusting your son's repertoire is surely part of the job you're paying him to do.

Save that for someone else.