Why do you think Shaw's friend (also an officer) protests against the use of the whip for punishing the alleged deserter (Denzel Washington) ? Common punishment for desertion (leaving the military camp) was to be flogged, or hit, but not necessarily with a whip. What about the whip is particularly bothersome?

Because the whip is a reminder to the black soldiers that they were slaves.

Explanation:

In the movie Glory, the 54th Massachusetts Infantry Regiment was one of the first all-black regiments in the Union Army commanded by Captain Robert Shaw. When Trip (Denzel Washington) allegedly deserts he is punished. Now usually the punishment for an alleged deserter in the army can be flogging with any other object. But using the whip is quite symbolic as these reminds the black soldiers that they were still slaves. This is the main reason why shaw's friend protested the use of a whip. This further justified when Denzel Washington's character, Trip, had his shirt torn off. You can see the marks from previous whipping on his back.

The reason Shaw's friend protests against the use of whip on the deserter, Trip (Denzel Washington) was because he saw it inappropriate considering the fact that Trip was an ex-slave that had been whipped mercilessly countless number of times before.

The whip is particularly bothersome because it leaves the victim with tears and scars on the body.

Also, it was a form of punishment used for slaves.