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How do you come to the conclusion why certain mechanisms are the way they are?
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This is a fascinating study in and of itself, but if you're curious (and you have the time!), the Clayden book I recommended to you has a good overview (Chapter 41). Short answer: kinetic studies, isotope effects and labeling, and structure-activity relationships (Hammett plots and Bronsted plots).
On a basic level, I think Dr. Iverson at UT Austin has compiled a good list of "rules" in o-chem that can help develop your intuition about arrow pushing:
Golden Rules of Chemistry