When you study psychology you don’t expect to sit around and do math all the time.
When you study biology you don’t expect to sit around and do math all the time.
When you study economics (especially if you actually want to become and economist) you do expect to sit around and do math all the time.
For many biologists and social scientists statistics classes must seem like a chore that has little to do with what they actually want to do. For economists statistics is just another one of their math tools.
My experience, though, is with applied macroeconomics. We'd derive models consistent with theory, then make sure we avoided a number of time series pitfalls (autocorrelation, mistaking cointegration for correlation, overspecifying a model) using a variety of statistical techniques.
Also, apologies for perpetuating the "arrogant economist" meme. Just reporting what I've experienced. :P