I guess there might be some good explanations as to why we call them critical point, but the root of your question is kind of pointless (no offense) :
You gave the definition of a critical point, when we define a word, especially in mathematics, it's a way to allow us to better communicate our ideas, but that's it.
I could say : "Wow do you see those three guys down below ? They form a nice three sided shape." But I use : "(...) they form a nice triangle.". Because we, as humans, already agreed on the definition of a triangle. We could have called them potatoes or scissors, the word itself doesn't matter, as long as we all agree on the meaning.
Shall I say it is critical that you understand this ? =)
EDIT to adress the comments :
chepner is on point, most mathematics words have latin or greek roots. I guess it might be confusing for english or germanic speaking people as it is more often than not completely different to what they use. When fleablood says "secant" is obscure to him, I think it's a good example : I speak french and here we got words like "sécateur" (which is a kind of scissor for plants) so it's easy to understand secant.
The word "pointless" I used seems not to be ideal and you have to put this on my lack of vocabulary. Again I didn't mean to offend.
For me, I understand "critical points" as "important, defining points" for a function, like if I had to describe the graph of a function in a sentence (not with the equation), those were the points I would name