There are 3 main reasons people may avoid empathy according to research:
It is too much effort and can be frustrating
If we have empathized too much already, we are less likely to do it later
If we have to empathize for a long time, we are less likely to choose to empathize
However...
We can decrease empathy avoidance by making the person feel like they are good at empathizing (or increasing their efficacy).
But, as good as this research is, there are important reasons to not take this study as the "truth." I'll explain more through the week!
Citation: Cameron, C. D., Hutcherson, C. A., Ferguson, A. M., Scheffer, J. A., Hadjiandreou, E., & Inzlicht, M. (2019). Empathy is hard work: People choose to avoid empathy because of its cognitive costs. Journal of Experimental Psychology: General, 148(6), 962. https://doi.org/10.1037/xge0000595