There's no such thing as an "insulting offer" unless you are dealing with a private sale. At a dealer, it's just business. Chuck out your offer. If it's too low, they're just not going to sell it to you. They will always counter, but expect it to be damned near asking price. They want to make a sale and you're in the showroom talking. That's the biggest obstacle to selling cars: getting them in the door.
This is the "dance" with selling cars, new or used. Dealers understand this. Offer, counter, offer, counter, offer, counter, etc.
If they get "insulted" at a dealer, then just walk out. They don't understand the business of selling and you are NOT going to enjoy any further dealings with them.Any and every dealer will at least try to "work" as seller to try and make a sale. Just that you are there talking means there's something for them to work on. If you're chucking out dollar values that are even close to the ballpark, they will keep at it to try and make a deal. They may call you a "jerk" to thier buddies after you leave, but who gives a rat's patootie what they think if you get a deal you are OK with?
If you're too far apart on a car, thank them for their time, shake the guy's hand and leave. It's a CAR, there's literally tens of thousands more of them kicking around out there.....and sometimes, you get a phone call in a week or two asking if you are still interested.......