This has happened to me a few times, in bigger or smaller scale, and I think it happens to many of us.
We as designers have the pleasure/curse of leaving quite a bit of us in every design.
When you have a client who, you feel, undermines your design decisions, how do keep that from affecting what you are doing?
Related question: How can I work with a client that doesn't know what they want?
You have a "thumbprint" client. This person must always change something, and feel like he's left his thumbprint on it, or he doesn't think he's done his job correctly.
I have a coping strategy I got from When Bad Relatives Happen to Good People. It's called "Setting a Budget."
A woman was upset because every time she went to her son's house for a weekend visit, things went wrong, plates were broken, the grandkid had a tantrum, clothing was ripped, etc., and the woman was miserable.
So the counselor asked her how many things usually went wrong in one of those weekend visits. "Oh, at least two dozen," she said. So the counselor told her to reset her expectations and budget for 24 lousy things to happen. After 24 lousy things, then she could be justified in being upset, because 24 lousy things was the norm.
The very next visit the son was astonished at how relaxed the woman was despite the chaos. "Oh, only 12 lousy things have happened, so I'm well under budget," she told him.
To apply that here, figure out the average number of thumbprints (changes) your client usually makes, and set that as your budget. Go in with that expectation.
After that number of changes, then you can justifiably feel frustrated or undermined.
There are actually a couple issues here.
If the client just repeatedly wants changes, as @LaurenIpsum posted, they are a "thumbprint" client. And you simply need to get to a point where you can separate yourself from the work and just do what they ask. I often have to tell myself "this is just what I do, not who I am." So changes aren't personal attacks on my skills or aesthetics.
I actually set things up for these type of clients. "do you like the blue or the red?", "Do you prefer the logo position in this layout or in this one?" Giving these types of client as many possible choices tends to help them feel vested and involved in the process and if you can provide directed choices you may be able to find a middle ground. One where they are making decisions so they feel they've made their mark, but you're also okay with the decisions they've made.
Yes, these clients take more work so I do adjust pricing accordingly. If I know I'm going to have to present an extra mock up every round so they can choose different items, then that extra time is factored. Of course, you may not know they are this type of client until after pricing has been agreed upon. So I keep track of the extra time I spend and will adjust future quotes for the client to make up for any loss. If they never return to me for work, then they got the better end of the deal.
The second matter is the word "insulting". I don't know if they are actually insulting you or just making so many changes you feel insulted (which happens to everyone I think). The customer is always right, but that does not mean they are always nice.
Are they truly insulting? I mean are they intentionally being demoralizing and condescending towards you above and beyond expressing they aren't happy with the work? This is a more serious matter to me. I won't deal with clients who are insulting. Well, let me rephrase -- I won't deal with insulting clients if financially I don't have to. If I come across a client who I feel has the perception that I'm somehow less than human or deserving of verbal attacks, I stop working with that client. I want a happy workplace and for me, life's just too short to be paid so I can be insulted. If they don't like the work, that's one thing. But attacking me personally is unforgivable to me.
If I ever hear the phrase, "My XXXX could have done that for only $x." My response is almost always "Oh, okay. Do you want your xxxx to do this project? Should I cease all work?" -- that tends to put an end to that insult very quickly.