The problem with always rounding halves up is that in doing so, you introduce a persistent bias in whatever calculations you do with the rounded number. If you’re adding a list of rounded numbers, for example, the sum will be biased high.
If you round halves to the nearest even number, though, the bias from upward roundings tends to be negated by an equal number of downward roundings. Overall, you get better results.
This article is technically about a change in PCalc, but it’s worth reading for these two paragraphs alone. I was always taught to round all halves upwards, but the round-to-even rule makes far more sense, especially when working with large sets of numbers. Consider me enlightened.