For an atheist - if an atheist is defined as 'lacking God belief' or 'believing God's existence is unlikely' - there's no obvious reason why swearing an oath to God is offensive, or really, something that should be rejected. It's at most a commitment to a being you don't think really exists, at least a symbolic act.
Now, if you're an anti-theist, we can start seeing reasons you'd get riled at the oath. But then you can't say that the oath is offensive to a mere atheist. You need something more.