Mowgli doesn't like to wear clothes, which makes sense since he's raised in the jungle by naked animals. Can you blame him? When Mowgli has to live with the Men, they force him to wear a cloth, "which annoyed him horribly" (5.24)—it just isn't his style, and he's accustomed to running naked through his days. Yet after squishing and skinning Shere Khan, Mowgli wears the tiger's skin with pride. What's the difference?
Well, Mowgli is proud of defeating Shere Khan. His roots are in the jungle, not with man, so while the loincloth is restrictive, the hide of Shere Khan represents freedom from the wannabe tyrant. In killing Shere Khan, Mowgli steps into his power, fulfilling Mother Wolf's prophecy from when he was younger, and proving his capability once and for all. And the tiger's hide is proof of this, his trophy, if you will, for coming into his own and shutting the naysayers up once and for all. So yeah, he wears that hide with pride.