A survey of websites provides a reasonable consensus: there are folk etymologies that do not seem to be accurate. These include a sailor whipped into quiet submission by a cat o' nine tails, a witches familiar in the shape of a cat stealing the ability to talk, and people having had their tongues cut out and fed to cats for some affront in an undesignated historic time.

These are almost certainly not correct. The earliest manifestation of the phrase in print apparently dates to 1881, Volume 53 of the US publication Ballou's Monthly Magazine, and it appears to have been a phrase that was initially associated with children.

The origin and inspiration for the phrase appears to be undetermined - and likely undeterminable - which is likely why the collective subreddit appears to have its tongue captured by a cat.

See this and this site, for example.

edit: my reference to /r/askhistorians having its tongue captured by a cat was in response to a clever, but inappropriate joke deleted - appropriately - by a mod.