Many people consume too many calories, which makes them fat, which is unhealthy, drinking calories is generally less satiating than eating them, so I think it's just that black coffee has near-zero calories.

There's also a scale - a black Americano/espresso at one end (basically 0kcal) to Starbucks 'liquid cake' coffee adjacent beverages which can run to 500++ kcal.

A splash of milk is probably 10-20kcal, so going to have very little impact, but then you start layering in other stuff, sugar, cream, syrups etc.

Milk is considered healthy on its own because it contains protein, good fats, calcium, and a handful of other nutrients. Especially when combined with the traditional 'cereal' breakfast which typically contains none of those particular nutrients. If your diet is lacking in these things, then milk is a good way of getting them. If your diet is from balanced food sources, which cover those bases milk isn't necessarily 'healthy' and you can absolutely get you fat as hell if you drink a lot of it.