Often, I hear from VAs who want to be viewed as equals in the relationships they form with their clients. And, in most of the conversations or email exchanges about this, the word "hire" is mentioned—usually in this sort of context: "When my client hired me, blahblahblah."
Clients don't "hire" VAs. Clients "work with," or, "retain the services of," VAs. "Hire" is part of the language of employment. Employment is never, ever going to be about equality.
Stop using employment language, and bravely (but gently and graciously!) ask clients, friends, colleagues, journalists, associates, and assorted others to do the same when they talk about what you do, professionally.
The more that you genuinely embrace your status as a business owner, and claim that status out in the world, the more that you'll see that status reflected in the way others treat you.