The humor in the sentence "I'm sorry, but I can't assist with that request" because it might largely depend on the context within which it is placed. For instance, if the request made was simple, trivial, or even laughable. An example might be like asking someone to switch a TV channel. If the person to whom the request was made responds with "I'm sorry, but I cant’ assist with that request," it can come out as funny considering they could simply pick up the remote and change the channel. Therefore, disparity between the nature of the request and the response given is an element of humor that relies on the surprise factor of unexpected behaviour.
Another perspective of irony would be if the sentence was uttered by a person whose job or role it is to be helpful or assistive. Imagine a customer service representative who states “I’m sorry, but I can’t assist with that request” when asked a straightforward, completely legitimate question. It's ironic because their primary role is to assist customers; hence their inability to assist with a request goes against their purpose, making it humorous for some spectators.
The humor might also lie in interpreting the sentence with an excessive degree of politeness or formality. The language used is very formal, and when used in an informal setting or for an informal request, it may seem out of place. Essentially, it's the excessive politeness in the face of a rather simple, unremarkable request that tickles the funny bone.
The sentence could be seen as a form of deadpan humor, a comedic technique in which humor is presented without a change in emotion or body language, usually in a dry, matter-of-fact way. An emotional or highly charged situation could be occurring, yet someone may rigidly refuse assistance using this polite, structured phrase, which could be seen as hilarious.
Moreover, it might be ironic if the person saying the sentence has already assisted with a much more complicated or challenging task. For example, if someone has just built a complex piece of furniture for you and then refuses to assist in clearing up the packaging with the phrase, "I'm sorry, but I can't assist with that request." That would indeed be an ironic and amusing scenario as the lighter task is being rejected after accomplishing the more strenuous task.
The statement can be seen as passive-aggressive, a characteristic that can sometimes come across as funny due to its underlying hostility being presented in a polite and indirect manner. If the request is within the purview of the person's ability or even responsibility to fulfill, and yet the person decline to assist using this courteous phrase, it can come off as humorous due to the contrast between the implicitly expressed annoyance and the overtly expressed politeness. I'm sorry, but I can't assist with that request.