What is the reasoning behind this?
If your goal is to reduce your variance, then a good number of times to run the cards is the LCD of your winning chances. For example, if you are 66% and he is 33%, you want to run it three times. If you are 75% and he is 25%, four times should be enough, etc. (it is "expected" that you will win the correct number of times). So seeing your cards might change the number of runs he agrees to (i.e. whether to give you less variance or more),
Furthermore, while revealing your cards shouldn't make a difference to your opponent, people aren't always logical (even players who use math heavily can have moments of weakness and irrationality).
Lastly, and this is just a general rule in poker, if you "know" your opponent wants you do X, it's usually the best idea to do the exact opposite (i.e. if it looks like they want you to call, fold... if they want you to fold, raise). It almost becomes instinct.