I’ve been in contractual quibbles before as the freelancer, so maybe I can shed some light on this. First, do you have a written contract? Written contracts are a must for both contractor and hiring entity. The written contract should spell out these details, such as dates, deliverables, payment terms, and other issues. If you don’t have a contract, I don’t know what to suggest. You’ll have to go back to your email exchanges to discuss semantics and whether he or you misunderstood.
If you do have a contract, you need to fine exactly what the area of disagreement is, like the exact clause… and from there offer a compromise. Maybe you do have to wait longer than expected, but hopefully you’ll get the work. You probably won’t be able to claim the money back unless. A) he hasn’t done all or part the work yet, and you’d like to end the contract, thus releasing the funds that were allocated to finish the work.. or B) you pursue the matter in small claims court (in your state if you in the U.S.).
If he’s already done the work, and you’d like your money back because he was late.. I’m afraid that’s usually not how it works. He can’t exchange the work and get his time back, he’s already spent it.. which is what you are paying for. A lot of people who work with freelancers want to treat it like a retail product.. “I tried it out, I don’t like it.. give me my money back”, or “I don’t like your work and it doesn’t satisfy me, now give me my money back”. Typically neither of those is reason to ask for your money back unless the freelancer totally failed to deliver to you. Preferences or expectations that weren’t outlined in the contract also usually not legitimate grounds to expect your money back.
If the freelancers is truly not fulfilling his contract, that both of you signed, which outlines the rules of engagement.. then you should probably mention “small claims court” if he’s not willing to negotiate or offer a compromise.