When in surplus or shortage, in order to achieve equilibrium price must change. I understand that. But what if when in surplus, suppliers choose to instead sell less, but for the same price? Vice versa for shortage.
In the standard competitive-market supply and demand model, the prediction is that, when an above-equilibrium price leads to surplus, prices will naturally fall. You're asking why suppliers don't just sell less at the same price instead, yes?
The basic reason why this doesn't happen is that doing this would require coordination on the part of the sellers, and there are too many of them to all work together.
Imagine, for example, that the equilibrium price is 10, but the current price is 15, leading to a surplus, with $Q_s=20$ and $Q_d=10$.
In your scenario, you end up with sellers agreeing to sell 10 units at a price of 15 each, and no more. However, at this high price, each seller will have an incentive to produce just a little more. One of the sellers, let's call her Jane, will sneak an 11th unit into the market, and either try to sell it as one of the ten units in the market at a price of 15, hoping that one of the other sellers will end up with an un-sellable unit, or Jane will try to take over the market by offering at a slightly lower price of 14 (which she can certainly afford to do - 14 is still much higher than her marginal cost).
For the plan to fall apart, there just has to be one person like Jane willing to work in their own interest against all the other sellers. And since there are by definition many many suppliers in the market, surely there's at least one Jane sitting around drooling at the thought of all those sales.
Most of the sellers would be better off overall if they were able to stick to an agreement to have a high-price and sell a low-quantity (after all, this is basically what monopolies and oligopolies do). But because there are so many competitors, each of whom has an individual incentive to break that agreement, the agreement is going to fall apart, leading prices to drop and quantity-traded to increase up to the equilibrium point.