>>44868568A lot of people were frustrated battling her Miltank, and then a lot of people were confused or even more frustrated by her crying instead of just handing you the badge.
Whitney really isn't all that bad, even if she is a little quirky. She's an emotions-first kind of person, and not very deep. When she loses battles, she had a quick cry, and then she feels better- no hard feelings.
Clair's a lot more complicated. She wants to prove herself the best dragon trainer, but she constantly has to live in the shadow of Lance. It doesn't matter that she's running the gym, or that she's considered the strongest gym leader in Johto, which are things that she wants to take pride in, because being compared to Lance is a weak spot that shatters her ability to positively perceive her accomplishments. What's more, she gets belittled by her clan, the people who raised and trained her, for not having fully understood their teachings.
Since her ego is already so fragile because of her situation, losing to a random prodigy child is just too much for her to bear, causing her to lash out and behave unreasonably. She ultimately starts getting better, but it's hard for her to drop the facade of haughtiness that she's been using for so long.