These are two sentences,first one means"the cock find no one want to compare beautiful with him",second one means "so he walk away with his head down",it should be like this"公鸡见谁也不跟他比美，只好垂着头往回走”

Thank you!^.^

This sentence reminds me of my book. I learned this article too.

thanks so much!

the rooster found out no one wanna have a beauty contest with him, he could do nothing but head back with his head bent down. (disappointed)