I think it's a rounding thing. Looking at an analog clock, you'll see at a glance that the hand is about halfway around the circle but it takes an additional processing step to determine whether it's 6:31 or 6:29. Looking at a digital clock, you'll see that it's 6:29 first and then it takes another step of processing to determine that 29 minutes is roughly halfway through the hour.

The way information is presented impacts how it is stored. If you look at a clock face and want to know what time it is it's very easy to visualize the passage of time as fractional because the time is presented to you without numbers being the primary focus and instead divisions. Mentally it is easier for you then to grapple with time as a fractional division. However, if instead of presenting the day as being divides into 2 portions of 12 hours, themselves divided into 12 subdivisions, those then further divided into 12 subdivisions of the 5tha of those divisions, you presented it as a simple read out the passage of time feels more like a linear stream mostly indistinguishable.

How we present time changes how we think about time, which then changes how we describe time.

Man language is cool...

I think it's because, visually, 3:15 puts the minute hand a quarter of the way around the clock face. Digital clocks don't have a corresponding visual.