When I did not like someone answer and I demoted that answer, my score was reduced by 1 - What is the idea behind this?
Down voting answers costs you 1 reputation point, this is status-bydesign.
The reasoning is that it makes revenge / retaliatory / otherwise abusive down voting less attractive, as discussed in a very early Stack Overflow podcast (circa 2008). Furthermore it emphasizes up voting over down voting, as does every other voting related mechanism we have (up votes earn you more rep than down votes cost you, etc).
That said, the penalty is too small to matter when you have legitimate reasons to down vote. It might matter a bit more to newer users, but I'm sure you having quite a lot of reputation wouldn't think twice before down voting a bad answer. And of course if you down vote sensibly and the community agrees with you, it's highly probable that the answer will be removed and your reputation will be refunded.
There used to be a reputation penalty when down voting questions as well. This changed a year ago:
Thus, to incentivize more balanced question voting, we are considering removing the -1 cost of casting a downvote on a question.
I don't know if it worked or not, but I enjoy free down votes on questions too much to care ;)