I am taking a course in Algebraic Topology. We are using Hatcher as a textbook. One of the main problems I am facing with the textbook is its level of rigour. Example: On Pg 10, Hatcher mentions in passing that $X^n/X^{n-1}$ is the wedge sum of n-spheres (here $X^n$ is the $n^{th}$ filtration of a CW-complex). While this is intuitively clear, it requires some work to prove. Another example is the proof(?) of the Cellular Boundary Formula on Pg 141. While I can follow what he says (and reproduce it in different contexts), it strikes me as a reason to believe the formula rather than a proof of that fact according to the idea of proof that I have become familiar with from earlier courses in Analysis and Algebra (also I do not think I'll be able to prove this fact at that level of rigour).
My question is: Is this level of rigour acceptable? I feel uncomfortable with the proofs Hatcher gives. But, should I be feeling uncomfortable? Looking back, I was never uncomfortable with the kind of justifications we used to give in high school calculus and this current discomfiture stems from the fact that I have taken a few courses in Analysis in between.