As Hatef already told you in his answer it is really the other way around!
Said that, the thing is a bit more complicated and it is much more context-dependent than Hatef said.
First of all, you said chef/host, so I guess you are interested in local customs in private situations. In that case it depends greatly on the situation. In general if you don't finish your food you may be asked why, especially if you didn't stop who served the food from filling your plate. You can get away with the explanation that you are already full, or that you are almost full, and the room left over in your stomach is for that tasty-looking cake you know will come next! :-)
Of course, if you are in an informal situation and you are in friendly relationships with the host, you could also say the truth and say that you wanted to try that food, but just discovered you didn't like it too much.
Note that in some parts of Italy, especially in the center and southern part of the country, especially in informal situations, it is customary to show hospitality by filling the plate of a guest to the brim! Or to serve a lunch with way too many different courses! So, if you are not a "great eater", be prepared to an effort! :-)
In a restaurant the things are not always as Hatef said. The description he gave is correct for high level restaurants (i.e. where waiters are dressed formally or wearing a uniform), but most commonly you won't be asked why you left something in your plate, unless you ate almost nothing. It is much more common, after you finish a course, to be kindly asked if everything was fine.
Moreover, in many pizzerias and restaurants "with an informal attitude" (for a lack of better term) you won't be treated with all such ceremonies. I don't mean they are rude, they simply are too busy and the personnel will just take the orders and deliver the dishes without much formalism (this is more frequent in those that are less expensive).
Yes, sometimes you find some chef that gets irritated if customers don't like his dishes, but it is something fairly uncommon, even in high level restaurants (for the price they charge, they usually don't want the client to get annoyed!).
BTW, "fare la scarpetta", which once was considered very rude because it was the hallmark of poor people (who were considered underlings, especially when Italy was still a monarchy), now is fairly customary (if you liked the food) and not frowned upon in most situations. Nowadays it is just considered a bit inelegant, especially in very formal situations. For example: a team of engineers or teachers going out for lunch during off time could well be caught doing "la scarpetta" and no-one will care. During a formal lunch where a CEO of a company meets potential industrial customers, probably you won't see that behavior.