Since you're playing all 6 strings at once, it makes sense to place your finger on one of the notes of the chord for each string. Therefore, for the C chord, you play CEGCE. It also gives you a nice full sound. If you didn't press C on the 2nd string and played it, you'd play a B which is not part of the C major chord....therefore you'd get a different sound from C. Not a bad sound but a different one.
And surely you’ll buy your pint cup !
and surely I’ll buy mine !
And we'll take a cup o’ kindness yet,
for auld lang syne.