It's important to respect other's talent because, we can't always be the best in everything. Sometimes other people are good at something that you are not, it doesn't always mean you have to compete with them all the time to be perfect.
In the poem the frog didn't respect the Nightingale's ability to sing and his jealousy was the reason of the death of the Nightingale. If he could just back down and enjoy her music, maybe even learn from her he could have been better at it; but he wanted to compete.
This is just an informal explanation.. hope this helps !!