I can't agree with your reading. One of each would be "you are required to make a back-up copy of the software and your computer data"; the singular has no other use. "Back-up copies of both" implies multiple copies of each.
Your point about contract construction seems much more convincing to me, and very sensible to boot - but it will doubtless vary from jurisdiction to jurisdiction. An EULA which requires me to do the impossible seems unwise to me, even though local contract law might save me from its insanities.