Squeaky has no respect for Mr. Pearson because he does not honor the concept of competition; instead, he wants to placate certain people and be popular. In short, Squeaky finds him weak-minded and lacking in integrity.

Mr. Pearson is a man who lacks imagination and sincerity. He mainly thinks of ways to make himself look better. Because the entries for the race have dropped in number since Squeaky usually wins it, Mr. Pearson encourages Squeaky to let someone else win:

“That new girl should give you a run for your money.” He looks around the park for Gretchen like a periscope in a submarine movie. “Wouldn’t it be a nice gesture if you were . . . to ahhh."

Squeaky is offended that Mr. Pearson would suggest to her that she allow someone else to win and not run her best. Because she is competitive, Squeaky has no intention of allowing anyone to simply win. Also, she can find no reason to allow a newcomer such as Gretchen, who is not her friend, to win.

More importantly, when Gretchen and Squeaky cross the finish line just seconds apart, three or four voices are heard together on the loudspeaker; then, Squeaky hears, 

...old Beanstalk arguing with the man on the loudspeaker and then a few others running their mouths about what the stopwatches say. 

Mr. Pearson is probably trying to convince the judges to give the win to Gretchen and deny Squeaky. Ironically, however, after Squeaky barely beats Gretchen, this newcomer and Squeaky start to develop a friendship following the event. Gretchen acknowledges Squeaky's win, nodding to her, while smiling. "And I smile. We stand there with this big smile of respect between us."