The Why Behind Sum of Squared Errors in a Linear Regression

I’m just starting to learn about linear regressions and was wondering why it is that we opt to minimize the sum of squared errors. I understand the squaring helps us balance positive and negative individual errors (so say e1 = -2 and e2 = 4, we’d consider them as both regular distances of 2 and 4 respectively before squaring them), however, I wonder why we don’t deal with minimizing the absolute value rather than the squares. If you square it, e2 has a relatively higher individual contribution to minimize than e1 compared to just the absolutely values (and do we want that?). I also wonder about decimal values. For instance, say we have e1 = 0.5 and e2 = 1.05, e1 will be weighted less when squared because 0.25 is less than 0.5 and e2 will be weighted more. Lastly, there is the case of e1 = 0.5 and e2 = 0.2. E1 is further away to start, but when you square it 0.25 is compared with 0.4. Anyway, just wondering why we do sum of squares Erie minimization rather than absolute value.