@SylvieLorxu The part before -cide denotes the species killed. Homi- stands for human, in this case, as well as the insecticide is for killing insects, for example. In Spanish we follow that rule for making more words: "raticida" for rat poison, etc. =)
Suicide comes from Latin, where sui means himself/herself. However, auto- comes from Greek and it means that you do the action, but not necessarily that the action is done on you.
I hope I have explained it well. =P