How does halving affect price?

I have tried my best to understand the affects of halving. From what i have read, it sounds to me like it only cuts the reward paid to miners in half.

So how does this directly affect the price? I guess if you consider that miners who sell their rewards would now reduce the amount to be sold by half, it means you are reducing the supply thus the supply and demand would cause the price to go up. But giving the total amount being sold on any given day, that the miners portion is probably a small percent then i wouldn't think the impact would be as much as i have read a lot of people are predicting.

Any insight would be very much appriciated.