Probability vs. Odds Ratio: Why do we even deal with odds ratios?

On page 137 in ISLR 2nd Edition, there is an example of a logistic regression model using a binary variable (1= yes student, 0= not a student) to predict if this person would be more or less likely to default. At the bottom, it shows when you plug in the coefficients and the respective dummy variable, the student has a 4.31% probability of default and the non student has a 2.92% probability of default.

I have 2 follow up questions:

1. Is it fair to say that the student has a 1.39% higher probability of default than the non-student? (=4.31-2.92). If no, why not?

2. If the above is fair, why do we even deal with odds ratios? The table shows that the student coefficient is 0.4049, which means e^0.4049 = 1.49915258, which means "There is a 49.9% increase in odds of a default occurring given that it is a student". Isn't it much easier to just say the probability of a student defaulting is 1.39% higher than a non-student?

Edit:

Loophole discovered. Looks like this doesn't work for continuous variables (example on pg 136), but OK for dummy variables. Looks like odds ratio relationships can be extrapolated for all 1 unit differences in feature X, but probability differences would only work for 2 specific X value differences:

• @Katsu You can always convert the predicted log odds to a probability and take differences on that scale. But you're right, the log odds have the benefit of being able to scale linearly so you know that every 1 unit change in the predictor yields a $\beta$ change in the log odds. This does not apply on the probability scale, but as I mentioned you can just convert to probability scales and report differences for desired levels of the covariates there. Commented Jan 5, 2023 at 5:25