Yeah. The downside of working with people is that many people are truly horrible. It sounds like your client is simply stealing from you, probably with some half-assed argument that is pure bullshit but designed to go in circles and make you crazy.

Going forward, remember to structure your work so that you minimize your exposure to this risk: get paid upfront, don't let the unpaid balance get too large, etc.

And try not to let it get under your skin. It's not you - it's them. And they are horrible.