obtrude

This verb carries a strong connotation of unwelcome intrusion and lack of social tact. It describes an action that is not merely noticed, but is perceived as an imposition or a violation of boundaries. When used regarding opinions or requests, it suggests a pushy or arrogant demeanor, contrasting with "suggest" or "offer," which imply a choice for the recipient.

In a physical sense, the word describes a protrusion that is obstructive or jarring. It evokes the image of something sticking out unexpectedly, creating a physical or visual hindrance. This usage is less common than the social sense but remains distinct in its focus on prominence and interference.