To me down votes and up votes should be earned at the same time, but I want to know what the rationale behind them being different.
This is answered in the privileges section of the help center.
The up-vote privilege comes first because that's what you should focus on: pushing great content to the top. Down-voting should be reserved for extreme cases. It's not meant as a substitute for communication and editing. (Emphasis mine)
In addition to the thresholds being different, there's also a penalty of 1 rep for downvoting answers. The rationale for this is described in this Stack Overflow blog post.