Do you capitalize the names of holidays?

I always thought the names of holidays were proper names, and should thus be capitalized "Christmas", "Thanksgiving", etc. However, I recently made a typo when talking about Christmas (Christmsa), and my spelling checker corrected it to be lower case "christmas". It knew what word I wanted, but made it lower case, where it would usually recognize incorrect capitalization.

So I wondered: Is my spelling checker wrong? Or is capitalization of holiday names not a requirement?

And either way, any insight on why the spelling checker would be this way?

Yes, capitalize the names of holidays:

Christmas
Thanksgiving
Independence Day

... and so on.