The sentence, "I'm sorry, I can't assist with that request," might be considered funny or ironic due to the context in which it is used. Ironic humor often comes from a contradiction between what is expected and what actually occurs. For instance, if this sentence is spoken by a robot in a sci-fi movie that was built to fulfill any command, the inability to perform a task would be a source of irony and hence, humor. The expectation is that the robot should be capable of any task, so when it expresses an inability, it creates an ironic situation.
The speaker's identity can also lend humor to this sentence. For instance, if a firefighter says, "I'm sorry, I can't assist with that request," when someone asks for help putting out a small fire, it’s funny because it opposes the norm that a firefighter is supposed to help with fires. This scenario creates situational irony where actions have an effect that is opposite from what was intended.
Additionally, the type of request also plays a role. The sentence could be seen as sarcastic or humorously indifferent if the request was something minor. For instance, if someone asked a professional chef to make a cup of instant noodles and the chef responded with "I'm sorry, I can't assist with that request." The incongruity between the professional skills of the chef and the simplicity of the task lends humor to the situation.
The phrase can also be seen as funny due to its formal register. It’s a phrase you might use in a business setting or customer service environment. If you use it in a casual, ordinary situation, such as declining to pass the remote control, its seriousness juxtaposed with the triviality of the situation can come across as humorous.
In certain instances, this phrase can also be considered as a form of self-deprecating humor. For example, if an individual known for their strength and fitness made this statement about not being able to open a jar lid, it would create an irony that could be funny.
Moreover, it can also be absurdly funny if said in response to an impossible, ridiculous request. Imagine if someone asked another to change the color of the sky and they responded with "I'm sorry, I can't assist with that request." The humor here lies in the outrageousness of the command and the dry, earnest response. I'm sorry, I can't assist with that request.