I know there are some people that get offended if you don't take the food they offer you. There are others who simply don't understand healthy eating and will criticize the foods that you're eating. Some people expect you to eat junk food or they won't stay your friend.
Peer pressure is usually tied in with talk about drugs, but can very easily be applied to food. There are relatives or co-workers who will beg you to eat certain food and when you tell them you don't eat that, they don't let it go. They hound you and hound you, as if they will convince you to partake in the food. I remember one job a while ago where I was pressured to eat junk food all the time. "Rich, have another candy..." "Finish this bag of candy..." Of course, I would always eat the food offered as I was obese and didn't care or think about the effects of eating too much junk food.
Recently, someone offered me a diet soda and they seemed confused that I no longer have aspartame. In fact, they acted as if I were trying to change them into giving up their soda. I have no interest in dictating to others what they should eat. I would rather offer my suggestions online about healthy eating. I'm not going to be offended if you're drinking a diet soda but please don't get on my case if I don't want one.
There is no reason to push others to change their eating lifestyles. It's fine to ask if you want a piece of cake, but entirely different to be offended if someone doesn't want it. I know some people who will avoid going to birthday parties, just because they are afraid of the pressure to eat the junk food.