Step 1: Understand the word.
"Obsequious" describes a person who is excessively eager to serve or please others, often in a fawning or servile manner to gain favor.
Step 2: Evaluate the options.
"Bold" means confident and assertive (near opposite); "argue" and "fight" are verbs and do not fit as synonyms for an adjective.
Step 3: Choose the synonym.
"Submissive" means readily yielding to the authority or will of others, making it the best match for obsequious. \[ \boxed{\text{submissive}} \]