Though that's a pretty big exception, no?
To my ears, 'symmetrical' is a normal word, 'symmetric' is, well, not. Something else. A dictionary artifact, perhaps. If anyone has a context where 'symmetric' sounds more natural, I'm prepared to be converted, but until then, I would say 'symmetric' is either a translation error by a non-native speaker or what Brian Garner calls a needless variant.
Someone (perhaps Pete under a different signature?) asked this same question a few days ago, Friday or Saturday, and I started making a list of words where -ic sounds right, vs. words where -ical sounds right, vs. words where there's a relatively free choice, or a difference in meaning. Unfortunately, the list very quickly got almost unmanageably too long -- I was only through about D or E in the alphabet before I started tearing my hair. However, if enough people were really interested, I could still try to shape it up into something that might at least give learners more examples to hold onto. It would probably take at least a couple more days.