State your case with full honesty. You only do a disservice to yourself to do otherwise.
Faculty who say that dropping their course is an insult to them have their heads in the wrong place. When they are roadblocks, request that your thesis advisor take your petition to the department chair for approval.
This all presumes that you have already gotten pre-approval from your thesis advisor to make this change in your program of study for this semester. In one sense, I should wonder with some experience why your thesis advisor did not warn you in advance not to take the course in the first place because you would have a harder workload this semester. Your insult here may be to have purposely ignored any such advice. Alternatively, you may be in a situations where you feel that you must do these type of things (schedule courses) on your own for whatever reason. I should wonder what new input as caused you to realize that you mis-judged your own abilities. Your insult here may be to have incorrectly pre-judged the work you would need in the course.
Lessons are sometimes best learned the hard way. In the case that you ignored your advisor, apologize and be honest about it. You may need his/her support to get the change done. In the case where you are working on your own, you may need to reflect carefully on what exactly you misjudged. Perhaps you do owe the instructor an apology because you are ducking out of the course that you thought would be easier (instead of dropping out of the course because you are faced with an unanticipated increase in the work load of your thesis). I am not judging either way, just providing a counter point for reflection.
Finally, you have presumably made yourself fully aware of whether/how dropping a course may impact (decrease) any financial support that you have. Alternatively, you are fully prepared to pay for a late registration fee should their be one to register now for a different course in order to re-fill you program of study in place of the dropped course.