According to economic theory, why does a business get less profit from lower prices as opposed to higher prices?I MEAN SOMETIMES A LOWER PRICE WILL...

The margin on a sale, otherwise known as the profit, may be very small. The price of anything must include that margin for profit. Minimizing the profit means lowering the price that may result in the price close to what the cost of a good or service might be to the business. If the price is less than or equal to cost, there is no profit and of course the business loses money and is out of business.

Price alters supply and demand. If the price increases, demand may lower. At the extreme, the price can be so high that demand approaches zero -- so there are few sales but large profit.

However, if the price decreases, demand may increase, and at the extreme, the price is so low that demand approaches infinity -- so there are many sales but small profit.

Furthermore, supply will be affected in the first case by having a glut of items; in the second, a scarcity.  But a glut tends to force price down; a scarcity forces it up!

Specifically, your question is contingent upon the item or service itself, and what value the market places upon it. Where cost is cheap -- consider a pencil for sale -- profit is small, but millions are sold.  Where cost is large -- like for a Rolls-Royce -- profit is large, but few are sold.