This is a "touchy" subject on this forum. Personally I am fine if a PC asks for my resume. I pick my battles and this is just isn't one of those issues that I really think is worth arguing over. Since we are virtual and the PC normally never meets us they just want something that makes them feel better about our qualifications.
And resumes are not just for employees as some others state. I have financial clients who get resumes from potential investors. They want to get a solid understanding of whom they are going into business with. I think this is the same idea when a PC asks a VA for a resume. Even if they FULLY understand the business relationship between a client and VA they still want to know with whom they are conducting business. It is just a good business practice.
Generally I initially start by having a PC view my profile on my website and do not volunteer my resume. However, if they still ask for a resume then I send them one. No big deal. It is only a big deal if we make it one. The PC is generally not trying to undervalue the VA or piss us off, they are just protecting a business investment.
Just my two cents. Ultimately it is a personal preference of each individual VA. If you are uncomfortable sending a resume, then don't. If it does not bother you then send it. It is your business and therefore your choice.
Best of Luck,