• Taking the quotients of a set by an equivalence relation - Having never seen how to construct $\mathbb{Z}$ from $\mathbb{N}$ or $\mathbb{Q}$ from $\mathbb{Z}$, the ritual of constructing $\mathbb{R}$ (if it is mentioned at all) appears completely alien and is forgotten immediately. The same student will likely forget (if they are able to understand in the first place) the first isomorphism theorem.
• Differential forms are mentioned explicitly but we treat the fickle beasts with great caution - If these unreal quantities are allowed to freely mix with numbers and variables, why must we be constantly told that dividing them is "purely formal"? Despite that various foundations of analysis have been made rigorous beginners to this subject do not benefit. Instead they are troubled by it and develop an allergic reaction to $\epsilon$.