I'll give a slightly different perspective. I work with TekSystems a lot. Let's imagine you're a customer and you go into a car dealership. You tell them you want a nice midsized sedan at a certain price level. If the sales person comes back and says "that's cool but I want you to lease this much nicer two door sports car. The horse power is double. And the price is 50% higher." You wouldn't be happy.

The client in this case is the company hiring an employee. They are asking for an FTE. They want to pay a certain salary. You are a consultant. You are asking for a certain hourly/daily/weekly/monthly rate. It's not that they don't like you. They just want something else. It's nothing personal.