I do understand what you are saying about 'giving in' to bullies, but I think that probably depends on the situation, and it is a bit hard to tell. He is upset, because of teasing. But it is hard to know (for him and for you) if the teasing is just about a smell, or is something more.
(can I just say that I am amazed at all this stinky egg stuff, I like eggs and don't think they smell
)
Kids senses tend to be stronger than adults and they will be silly/overreact to smells, but it can be a simple as that.
When I was teaching we had a child in the class who smelt, very poor home situation, dirty smelly child. The others complained, were unkind, wouldn't go near him.
Periodically social services went in and cleaned the family up. For a couple of weeks afterwards the class accepted him and played with him, no comments, or anything. As the smell returned, the kids pulled away. The teasing was simply the smell, and I think that is quite common.
I think that some kids like to go against the crowd. One boy in dds class has shoulder length blonde curls. He is the only one in the school with long hair. He likes to take a stand on something and not worry about what others think (he would take in the egg and eat it with a flourish). Others are very aware of 'fitting in' and want everything to be the same as everyone else so they don't stand out. ds is like this, to my surprise. He wouldn't take a hat on a school trip until he got to school and found that others were actually wearing them. Ds would remove the egg from his lunchbox and hide it, so as to be the same as everyone else.
With a child like this, I will go a long way to help them do what they want to fit in. They feel more comfortable, which then boosts their confidence, so that at some point they will take a stand on something they feel strongly about.
Let ds choose what he feels comfortable with.