The question posed by the teacher or professor is misleading. Yes, increased competition is generally a result of increased demand. That, however, does not mean the firm in question welcomes competition. As I noted in my first response, the firm to which you refer would prefer to have the market to itself. That way, it reaps the greatest profits because it has no competition. The more competition, the lower the revenue and profits because consumers have more choices and may choose the other firms. Too many firms competing for the same consumers results in minimal profits for each firm, as the revenue is spread among those many companies. So, a firm without competition wants to remain without competition because consumers have no other choice but to purchase that firm's product. All of the revenue and profits go to that one company. As other companies begin to compete with the original firm, prices go down and, with it, profits. It's the basic law of supply and demand.
While it is true that the emergence of competing businesses often indicates an increase in demand, existing firms rarely celebrate the introduction into the marketplace of competitors. In general, most firms would love to enjoy a monopoly within their market. That way, they could set prices strictly according to demand without regard for competition that would, by definition, depress those prices. If the market is large enough to support multiple competitors, then prices and, consequently, profits, can still remain high. As competing firms enter the market, however, the depressive effect on prices and profits kicks in. Consumers enjoy competition precisely because it does often translate to lower prices and better service and product quality. A business that has enjoyed a major share of a market, or even a monopoly, might be perfectly capable of competing with other businesses, but it would prefer the absence of that competition so that consumers would have no alternative if they desire the product or service in question. For this reason, the statement is false.