Anything treasonous involves a betrayal, particularly of your country. Your sister might consider it treasonous if you tell your parents she skipped school to go to the beach.
When we betray our friends or families, that's personally treasonous. To betray your country is legally treasonous, since it's a punishable crime. It would be treasonous for a CIA agent to hand over U.S. secrets to an enemy spy—and the root of treasonous is the Latin verb tradere, "to hand over or betray."