This question raises more questions here.
Please, keep politics totally separated of safety and answer here political reasons not to cycle in some countries. The user Ambo100's earlier example about Sharia law and two men's prosecution is unverified. Freiheit offered better example (I think I have heard this somewhere but haven't verified it myself):
in Saudi Arabia, women are not allowed to ride bicycles (or drive cars)
Anything like that please gather here.