爭先恐後

striving to be first and fearing to be last (idiom); outdoing one another

to strive for / to vie for / to argue or debate / deficient or lacking (dialect) / how or what (literary)

to compete to be first / to contest first place

early / prior / former / in advance / first

afraid / frightened / to fear

back / behind / rear / afterwards / after / later / post-