As one develops respect for their body, it is natural to wish to only expose it for those they are comfortable/intimate with. Trusted medical professionals, family members, and spouses usually are people with whom you can be more relaxed with your modesty with, as it has been throughout history. This is why many poor, body-shamed girls wear clothing that is considered provocative, because they feel the need to be attractive to be noticed (it should be noted that modesty problems exist with men, too, if less of a widespread problem). As they are appreciated for their personalities, they will naturally be more reserved with their appearance when around others with whom they do not feel the need to be intimate. Our bodies are special, which is WHY it's important to cover them, when not around our special someone.
The more we love our bodies, the more we want to save them for intimate loved ones who we know will respect them and not objectify them. There is a reason why modesty tends to be more relaxed in private with family, spouses, and trusted medical professionals. There is also a reason why many of the poor girls being body-shamed nowadays feel the need to expose themselves to get attention (this can also be a problem with boys, but not as big of one, especially as they have different problems along these lines). When people start respecting women for who they are and encouraging confidence, they will care less about trying to attract and more about building relationships without the need to expose themselves. Modern fashion reflects this, so not all girls that dress this way do it out of these reasons, but the root of their fashion trends are objectification (and some like to not be as hot during the summer... But some revealing fashion trends aren't based off of this).
Well yes you can teach modesty without body shaming. How? Well you have to at least try with out using words such as "fat" or "big". I mean personally I kinda of am. But never think bad about yourself. I just think you should move on about words like that and never let come in your way!
Having modesty certainly does not entail thinking that there is something shameful about your body. It's quite the opposite. A modest person does not flaunt their body, and shows respect for the people around them who may not want to see another person's body displayed for everyone to see. People who are modest are respectful of the sensitivities of others. There is nothing shameful about your body, but everyone does not care to see it, and if you respect yourself you will not put your body on public display.
I'm not sure that modesty needs to be "taught" at all; but if it does, it should absolutely be taught without body-shaming. Body-shaming is plainly a damaging thing and stupid, to boot. If a person is respected, from the earliest age, they will grow up with a healthy degree of modesty naturally.
The value of modesty can be taught without body shaming. Of course, modesty extends far beyond just body issues and is a lot more involved with how a person looks at the world as a whole. That can be comprehensively taught. It just depends on the type of curriculum used.
Body shaming and modesty are two very different things. If anything Modesty shows pride in ones body. There is nothing wrong with the human body and no one should ever feel there is something wrong with the way they are. Modesty isn't so much an issue of shame as it is about having class and dignity and respect for ones self.
Modesty doesn't go hand in hand with the idea that parts of the human body are wrong or that it's negative to show them off. You can teach modesty by teaching self respect and the idea that you don't have to show off your body for attention rather than teaching that it's just plain gross or wrong.