The first question (the one about algebra) may not be ideal for the site, but what significantly sets it apart from the second question in my mind is that it asks for at least mostly-objective answers: namely, "is at least some amount of graduate-level algebra a basic part of a mathematical education?" and "what are some topics that relate algebra to differential geometry or differential equations?"
Regarding the second question, I agree with Dylan Moreland's comment: "Is it a survey? Is it crowd-sourced soul-searching? Those are both important endeavors but this doesn't seem like the place for them."
I think that the appropriateness of the question "why study X?" depends entirely on the context of the word "why". The first question is clearly asked by someone who is comfortable with the idea that mathematics as a subject is worth studying, and their question is just asking about whether certain topics in algebra are regarded as a basic part of a mathematical education, and how algebra relates to topics they are more interested in. The second question is asked by someone who regards "the professor told you to" or "you have to take something" as possible answers; thus, I take the meaning of "why" in the second question to be the personal / unanswerable kind of "why" - as mixedmath comments, "Why do you do anything?" That's what makes the second question non-constructive, and closure-worthy in my opinion. Dylan is correct that "off-topic" was probably not the best choice of closure reason.