His father is so obsessed with his work in the Ministry that it's like his work is more significant than his family. But then, you asked the specific reason of why was Barty Crouch Jr. a Death Eater?
There is no specific reason based on what I read in book four.
It all just leads to a fake Mad-Eye who wants the Dark Lord to be pleased with him after what he did to help Voldemort to find a way through to Harry, to rise again, and to kill.
'The Dark Lord and I have much in common. Both of us, for instance, had very disappointing fathers...very disappointing indeed. Both of us suffered the indignity, Harry, of being named after those fathers. Both of us had the pleasure...the very great pleasure...of killing our fathers, to ensure the continued rise of the Dark Order!'
Barty Crouch Jr. - Harry Potter and the Goblet of Fire, Chapter 35
The reason stated above could have been one contributing factor. Voldemort was born with a Muggle father who abandoned him and his mother after the love potion's effects wore off. Barty Crouch Jr's hatred for his father worsened every day, just like what happened with Tom, and it can be guessed that Barty Crouch Jr possibly got used to doing Dark things every day that lead him to become a Death Eater - after his grudge and rebellion against his father.
As was mentioned, he was a highly accomplished student. We still don't know how or what plans he had. Just like Tom Riddle, he was great at school - but eventually Riddle became Voldemort.
Clarification: Barty Crouch Jr. possibly hated his father and turned out to be a rebel, because his father's methods in sentencing him to Azkaban were unfair. He uses unforgivable curses and, at the same time, sentences people to Azkaban without proof or evidence. His son would have thought that these accusations were ridiculous, unfair, and highly unbefitting of a Ministry worker.
But most of all, the characters in the story seem to conclude that Crouch Jr's decision was because his father was known for not guarding and spending proper time with him.