Why is it Bad to Discretize a Continuous Variable? I am an MBA Student taking courses in statistics.  I was doing some reading online and came across Carstensen (2020), which I unfortunately do not have access to.
This article suggests that "categorizing quantitative variable" is bad - but I am not sure why this is. Our professor in our statistics courses showed us examples where a decision tree was fit to some data where the dependent variable was originally continuous, but then "binned" into groups. In his example, this strategy seemed to work fine - but some other references are suggesting that this is bad practice.
Can someone please explain why doing this might not be ideal? I understand that if you make arbitrary bins that this could lead to problems and lose information in the process - but if the bins are made carefully and rigorously tested, why is it bad to "categorize quantitative variables"?

A different issue is that the categorical model may be unnecessarily hard to fit, caused by the philosophical mismatch of the model to the problem.
Suppose I have a large spring. The farther I pull it, $x$, the more force it exerts, $y$. This is an extremely straightforward continuous relationship -- pull a bit farther, feel a bit more force. I could fit a model $y = ax$ with just one parameter, $a$. If Hooke's law applies, then just a couple data points will give me a very accurate estimate of $a$.
Now consider the categorical approach. I could break distances up into one hundred buckets, $x \in [0,1]$, $x \in [1,2]$, ..., $x \in [99,100]$. Now I have a model with at least one hundred parameters. It is capable of modeling many relationships that I know are impossible, such as the force going up and back down and back up etc. as the spring is stretched farther and farther. I may need hundreds or thousands of data points to fit the model. And it still won't predict very accurately at resolutions below $1$.
To fix this, I could just use a couple buckets, $x \in [0,50]$ and $x \in [50,100]$. Now I don't need as much data and my model is simple, but very inaccurate.
