Sometimes we are tempted to assess a relationship of X1 with Y while controlling for X2, but it would be a mistake, because X2 is not merely correlated with Y -- it is more closely associated than that. This sort of X2 is part and parcel of Y; it is part of what "makes Y Y"; it is difficult to meaningfully disentangle from Y. One might say that without the X2 component Y is no longer fully itself.
Examples: Regressing high school grades (Y) on time spent practicing music (X1) while controlling for standardized test scores such as SAT or ACT (X2). Regressing anxiety (Y) on daily number of hours of sleep (X1) while controlling for intake of (need for) anxiety medication (X2).
Are there any common terms for this sort of close relationship that goes beyond correlation and that should not be partialled out?
EDIT:
I'm talking about explanatory, not predictive, analysis. E.g., the point is not to account for the music-academic-achievement relationship over and above what can be predicted by another indicator of academic achievement (test scores), but rather to explain the music-academic-achievement relationship itself.
Elazar Pedhazur in Multiple Regression in Behavioral Research (1997, p. 172) describes the error as "partialing a relation out of itself." Others might call it erroneously controlling for what is in fact a parallel measure of Y and in the process losing the ability to accurately assess the relationship between X1 and Y.
EDIT: An example from the field of health care quality (still without the sort of term I'm looking for) is the following from https://www.ahajournals.org/doi/10.1161/CIRCOUTCOMES.108.832949:
"The data selected for incorporation into a model will differ between a measure to predict an individual’s risk of readmission and a measure to profile hospitals on their readmission rates. Development of a readmission prediction model for individual patients should include all relevant information, including in-hospital events and discharge disposition. However, in developing a profiling model to assess the performance of hospitals by readmission rates, patient-level characteristics must be carefully selected to focus on those present on admission and to prevent inclusion of factors such as in-hospital complications, length of stay, and discharge disposition. Accounting for such characteristics could inappropriately risk-standardize hospital performance for the very differences in quality and efficiency that profiling attempts to measure.[44] Poorly constructed models could therefore undermine the very goal of focusing on readmission (ie, promotion of high-quality efficient care)."