I have never fired a student. I was a one man flight school with an office, insurance and my own mouth to feed. I was willing to work with anyone. I had a good group of focused and motivated students I was able to get their ratings fast, I also had the group of wanna-be-pilot losers. Its a sad way to describe them but I somehow attracted the people that wanted to be a pilot when they grew up, but did not have the focus or maturity to ever make it happen. As an example one student who started flying at 18 was still working on his solo at his mid 20s. He'd give me a big chunk of money (to him) and then show up late and unprepared, then spend a lot of the session talking about things other than aviation.
I would sit them down for an LF conversation. Subjects covered: I have you scheduled for two hours, I will be billing you for two hours, you can show up when you want and talk about what you want. I would describe how hard it is to become a career pilot. A college degree is easier than an aviation career, this is not an easy way out. I am willing to take your money but I won't sign you off for anything until you are up to my standards. If you are not ready to focus and commit to this you should quit wasting your money, spend it on your car, in a bar or on your flight sim computer. A few I managed to get them a rating, some quit, some just kept muddling along. Even though I needed the income flying with people who did not put the effort into it, was the worst part of my day and I often came home complaining to my GF.
Among the people I never signed off for anything was my business partner. After owning a flight school for 3 years he was never more than a student pilot. I had to cancel his checkride at least 2 times that I can remember because he did not show up for the 3 flights I told him it would take to get him ready. He'd call up 9 months later expecting to be ready for a checkride with one more flight.
Unless you are unprepared, or unsafe I feel your CFI owed it to you to complete your training and not waste your money. NAFI has a code of conduct, probably worth the paper it is written on. Your club may also have a way to make sure this guy does not give someone else the run around. Look for more feedback from your instructors after each flight, you should have realized this guy was impatient with you and looked for another instructor before it came to this. I would suggest staying away from grumpy old instructors. Come in very focused and knock out the sign off with a new instructor and move on.