Thats not an accurate statement.
Non-profits DO make/earn profits. Entities are classed as "non-profit" for the purpose of being tax-exempt for income tax purposes and are allowed to be so classified if none of the profits of the entity are distributed to any shareholders, members, owners or those who appear to be shareholder, members or owners, etc. (For example, dividends).
Non-profts want profits as much as any for-profit entity, to use for its corporate purposes. Hence, what would be income of a non-profit, revenue in excess of its costs/operating expenses, is not taxed so long as it is put to the exempt purpose (i.e., charitable, religious, educational, scientific, or other purposes) instead of being distributed to owners, shareholders, etc., of the corporation, as would be the case in a so-called "For-Profit" entity.
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