Analog clocks lend themselves better to thinking in fractions of an hour or day, like this post is talking about, as an hour and a half day are both represented as a circle
Digital clocks lend themselves better to thinking in terms of number of minutes and hours directly. When working numerically, fractions of 60 are generally less intuitive, and fractions of 12 often so as well. Most people who don’t work with angles often think of fractions in terms of percent, or powers of two.
“Quarter past” kind of tweaks the brain wrong when a quarter is intuitively 25.