Over the course of my studies I often encounter phrases in reference material of the type "and this avoids the need for using $\epsilon$, $\delta$ definitions" or "by this we can omit those complicated $\epsilon, \delta$ arguments", etc. In other words performing stunts in order to get around $\epsilon, \delta$. I've seen enough of this to think that it should be categorized as epsilondeltophobia, if you all will permit. Personally, I was thrilled to learn definitions in these terms because it was one of the first rigorous definitions given to me, all in terms of quantifier logic, and it was used for very fundamental things whose real meaning I always wondered about. In the beginning of course I didn't have a clue how to use the language, but I loved it anyways because it was like, "wooow, deep maan". Not to mention that later on, I began to see that all of the higher-order constructions that were built upon $\epsilon, \delta$-objects worked out perfectly, giving me more satisfaction that whoever came up with $\epsilon, \delta$ language knew what they were doing. So I'm not saying that it's not ok to develop an epsilondeltophobia, as we all do naturally in the beginning...but textbooks (some) seem to promote this fear, even some teachers, and this is what I'm not happy about. I think $\epsilon, \delta$ is great.
Question: who thinks likewise? oppositely?
Edit: I don't want this to come off as a pedantic "rigor or death" statement, or as a suggestion that first courses on calculus should always include $\epsilon, \delta$ (although maybe yes in mathematics). I'm just against the predisposal to it in a negative way.