Unlike many (but not all) other animals, humans spend considerable time in close proximity to other humans in enclosed spaces. If you are pungent, other people in an enclosed space with you will not appreciate your smell. I've done quite a few multi week hikes with only fresh water bathing (no soap, no deodorant) with others (2-18 other people). During the hikes we are outdoors and although we gather reasonably close (less than 1m, or a couple of feet) around a campfire or common place to eat it isn't often you'd be offended by someone else's smell. At the end of these hikes when we first get back to civilisation and are in an enclosed space again - you bet we suddenly notice how much we stink.

Many humans cross paths with hundreds to thousands of other humans every day and the set of people interacted can have great variability across days. Growing up we were taught at home and in school how important it is to regularly wash your hands. The only other examples of such a high level of social mingling for other species that springs to mind are insects swarms/hives/nests and when there are plagues (mice, locusts etc). Unlike these groups, humans are unique in having a very high degree of share tool use (door handles, public seating for transport, cross walk and lift buttons), so there is a huge potential for cross contamination. Bathing and washing with soap is probably one of the key reasons we are able to live in cities the way we do without regular disease epidemics.