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"?

Others answers have discussed how discretization throws away information, which can hide effects which would be discovered if the continuous data were used. But sometimes the loss of information actually creates illusory effects in the data!
For example, suppose I'm trying to determine if a particular Northern species of bird migrates south in the winter. In the first week of November, I tag each bird caught and released from a research site at, say, $47.5^\circ$ North latitude. To get a larger sample size, I also tag the birds from a more northern site, at $51^\circ$ North latitude. Then I use the tags to locate the birds in December, seeing if they trend south as it gets colder.
Suppose that in reality, the birds don't migrate at all, but just mill about, some heading south, some north. The continuous data would reveal that there is no migratory trend whatsoever, only random displacements between November and December. But I decide (foolishly) to discretize my data into bins $5^\circ$ across. None of the birds I tagged made it below $40^\circ$ or above $60^\circ$, so I break my sample range into four bins, $40^\circ$-$45^\circ$, $45^\circ$-$50^\circ$, $50^\circ$-$55^\circ$, and $55^\circ$-$60^\circ$. This feels like a natural discretization to me, as the ranges have nice, round-number endpoints.
The first site is in the center of a range, so it doesn't cause me any problems. Most of the birds tagged at the $47.5^\circ$ site stay in the $45^\circ$-$50^\circ$ bin, but some of the outliers end up in both the $40^\circ$-$45^\circ$ and $50^\circ$-$55^\circ$ bins. However, the $51^\circ$ site is close to the bottom of its bin, so birds tagged there are much more likely to randomly move to the bin below than the bin above. I notice this pattern in my data, and wrongly conclude that the northern population of birds tend to travel south during November.
When I publish my results in an esteemed ornithology journal, I don't include the latitudes at which the birds were tagged, only the bin in which they were tagged. I do include statistical tests, including a $p$-value below 0.05, which supports the claim that the birds trend into southern bins during Novemeber. My readers have no way of knowing that the reason for this trend is that my discretization biased my methodology, and are convinced that I have discovered a real phenomenon.
