Solution 1:

When people say I met him on the street, they are usually not referring to a specific street. Instead, they mean I met him outside in the city as opposed to I met him at a party or I met him at a friends house.

Basically, they are using "the street" to refer to "the city/urban environment"

They are (almost always) not referring to an actual street because that would usually be irrelevant.

The similar usage is when people say He lived on the street. They are not necessarily referring to an actual street (or group of streets) but they actually mean he did not have a home to live in.

EDIT: as @medica mentioned in the comments section, "the street" is a single composition that you cannot take apart.