Is "whatever" an impolite word? And is sighing rude?

I’m analyzing a conversation for my thesis. One person said “whatever” a lot when he wanted to change the subject and he sighed when he felt offended. Then at one point the other person said he shouldn’t sigh too much because “that’s like little upset toddler behavior”, and “whatever” is a rude word. This throws me off. Are they universally unacceptable behavior, or was it just the woman who was personally offended by the behavior?