I use a shaving mug and brush because it reminds me of my grandfathers. The odd part of that is I never saw either of them use one or saw one in their houses. By the time I was old enough to notice such things, Gillette Foamy was on the market, and both my grandfathers switched quickly to the easier form, as most men did. They were neither sentimental nor hidebound about such things. They must have used a mug and a brush earlier, but before my time.
So I am reminded of them for false reasons, but the act has repeated so many times its origin is superfluous. Shaving mug = grandfathers. We do not remember events directly - we remember the last time we remembered - and thus bend memories over time. Reminiscing with others, photos, and old documents can correct our slippage somewhat.
For the record, I do not use a double-edged razor, and certainly not a straight razor. I am quite clumsy, and don't want to associate my grandfathers with bleeding and disfiguring myself.