Nine months ago I agreed to exchange my services as a designer in return for free consultations from the client (who is a doctor). We agreed that we would exchange our services by matching hours for hours (eg. I would give him 12 hours of my service in exchange for 12 hours of his consultation).
During the course of this period, I had been in for a few consultations, roughly amounting to 4 hours of his service rendered to me. Meanwhile he had made some small steps with beginning the design project, but it was moving very slowly.
Today I get an email stating that he worked with another designer to do the job, and since I haven't performed any work for him, he's chosen to invoice me for the hours he's rendered to me. We have no contract but we have a series of emails outlining what would be exchanged, and money wasn't stated as a form of potential compensation.
I am wondering if the client has the right to claim for monetary compensation if they are backing out of the arrangement, or if I have some kind of power to offer an exchange of other services as originally agreed?
Doesn't this also amount to a breach of an agreement on their side, and therefore they aren't entitled to anything at all as a result?