My interpretation of the condition $P=MC$ is that a firm's cost of producing one additional good should be equal to the firm's price. This means that the next item a the firm produces won't yield any profit to the firm. What's the point of producing this additional unit? Do you have a hands-on explanation?
You should keep in mind that the definition of profit in economics is not the same as in accounting. In particular, economists always deduct opportunity cost from accounting profits, and the price = MC formula has to be interpreted in this way.
For example, let's say you are a self-employed web-developer and you may make a profit in an accounting sense. Economists will subtract from this accounting profit the opportunity cost of not working elsewhere. Looking at it this way, the profit of a self-employed web-developer is just a wage he pays to himself.
The same is true for larger firms. Those firms usually pay out accounting profits to their shareholders. Economists would interpret this as the cost of using the equity capital provided by owners.
If you take the price of a product as given, which is fairly conventional assumption, the profit for the next product you sell is equal to that price minus your marginal cost of producing and delivering that product to the consumer. Ofcourse you do not want to make a loss by selling a product, so you will only sell products as long as your marginal cost is lower than the price. Or, untill they are equal.
Note that this is not a sufficient condition, an agent will only produce if this given price is higher than its average costs.
The condition P=MC refers to the price corresponding to the maximum quantity of a commodity produced/supplied by a producer-supplier that is earning profits of net-zero or more and is not price-setting.
Your question is "if the price of commodity X equals the marginal cost of producing X then why produce more X?" The answer is that it is not rational to produce more X.
The condition P=MC refers to the greatest price a profit-maximzing producer can set for what it produces if that producer faces a perfectly competitive market, because producers/suppliers cannot price-set in a perfectly competitive market but will not produce for profits less than net-zero.
Assuming no price-setting: ceteris paribus, if firms A and B have the same marginal cost and enjoy the same profit but A faces a perfectly competitive market and B is a monopoly then B produces less than A, which increases the price of the commodity it produces.
Suppose you produce a quantity $q$ where $p>MC$. This means that if you were to increase your quantity to $q+dq$ then your revenue would increase by $p\cdot dq$ and your costs would increase by $MC\cdot dq$. Since $$p>MC\implies p\cdot dq>MC\cdot dq$$ the result is an increase in your profit, so quantity $q$ can't have been optimal.
Likewise, suppose you produce a quantity $q$ where $p<MC$. This means that if you were to decrease your quantity to $q-dq$ then your revenue would fall by $p\cdot dq$ and your costs would fall by $MC\cdot dq$. Since $$p<MC\implies p\cdot dq<MC\cdot dq$$ the result is an increase in your profit, so quantity $q$ can't have been optimal.
Thus we see that producing at any point where $p\neq MC$ is not optimal.
When we produce where $p=MC$ this argument breaks. An increase in quantity causes profit to change by $(p-MC)dq=0$ so I can't do any better by making a small change to quantity. This is a necessary condition for the current quantity to be optimal.
You can think about it as follows:
$p$ (the price) reflects consumers' demand for that good, whereas $MC$ reflects producer's supply for that product
If $p>MC$ it means that consumers demand more for that good, so the producer has an incentive to increase the supply. On the other hand, if $p<MC$ it means that producer produces more product than consumers demand. Since the production of the good is costly, the producer has an incentive to decrease the supply.
At $p=MC$, neither consumers nor the firms have an incentive to demand (produce) an additional unit of the product, and hence the quantity of the good that satisfies the condition $p=MC$ is said to be optimal.