That only shows how you have to choose words carefully.
Of course you must be professional and try your best to explain, but people who hire other people have most of the time not the slightest idea what they need to contribute. It is in all professions like that.
Educating them is fine as long as the customer has the time and/or interest. They hire you and want you to wave that magic wand and make everything alright and perfect for them without having to get involved too much. That is your job in their eyes and it is right to think that. And yes, they are ignorant often and underestimate what things will cost in time and money, but again, it is so in all service oriented jobs.
Add to that the horrible and mediocre taste level, the low percentage of income most sites will generate as opposed to a physical presents for those clients, it is hard to convince them to pay more than they have budgeted based on their perception. Combine all those points and you end up where you are today in this industry. I do not see a change anytime soon, there are too many parallels in other industries to point to the same mentality.
Look at architecture as an example. The horror that is committed with cookie cutter places and shoddy workmanship. It can all be done better and people are mostly aware of it, but they could not afford to buy a place that would cost five times as much, but they have been sold and bought the illusion that the place would be almost as good as the real one. So it is with websites. People who get stung by unprofessional "professionals" have just bought their own unrealistic dream. And so it is and will be, that is how most humans live in all their endeavors.
Job satisfaction always comes from being in the driver's seat, and I agree that you should try to educate the client as much as is reasonable. When a client is too inflexible or unwilling, I personally would part ways. That is what you have to find out before you get too deeply involved. You have to become a reader of people to avoid getting trapped. Many things can indicate to you in the first interview if you can work with this person/firm. Formulate your questions in such a way that the client will reveal to you what you need to know before you start. Unreasonable expectations will float right to the top that way.

