Many so-called anti-oxidants are also pro-oxidants. This is a good thing since we need a balance of pro and anti-oxidants to function optimally. Pro-oxidants are an integral part of our front line immune defence against nasty invaders.
In any event, cycling vitamin C means just that. Maybe take 100mg per day for a week, then 500mg per day for the next week, then have a weekend off. Bump it up to 1000-2000mg per day if you feel a cold coming on, and drop back down to none or 100mg per day after you've beaten your cold. If you eat lots of fruits or veggies, then have entire weeks without any extra vitamin C intake. There are no rules in this field of vitamin supps. All we know is that if you chronically take the same high dose, that intestinal transporters will down regulate, effectively reducing your uptake of vitamin c. Best to avoid this so you can have good uptake WHEN YOU NEED IT like to fight a specific infection.