To be honest, I'm sure I thought some of those same things in 11th grade. I'm sure many in the class agreed with her. While my initial reaction was to defend the need to analyze poetry, what I realized was that reading into things isn't unique to poetry. We all do this about everything, everyday. I asked the class to consider the Richard Sherman incident from Sunday. How many times have his simple words been bounced around the internet and interpretation and meaning been sprung from his simple outburst? Entire TV shows have dedicated hours to trying to figure out if he should or shouldn't have said it.
Meanwhile, Twitter is filled with allusions, symbols, tone, and subtweets. Facebook is rampant with passive-agressive attention-seeking and verbal irony. (Maybe this is why Snapchat is popular...there's no time to analyze it because it's gone instantly.) Even everyday conversation is all about analysis. We interpret meaning and hidden meaning, text and subtext, tone and mood constantly without thinking about it. Reading poetry may seem arbitrary, and a bit confusing at times, but its not less confusing than what we analyze in our own free time. Imagine explaining a football strategy to an alien. They'd like respond "who cares, it's just a game, why bother thinking about it so much?" And then you'd say "Wow, you speak English!"
So the next time you're sick of analyzing poems, remember...this is just another sub-culture you don't quite understand. There's few better people to analyze hidden meaning and understand unspoken rules than teenagers.
Analysis, actually, is...all around.