How can you explain the MR=MC equation as the PROFIT MAXIMIZING output level?

Start with three concepts or laws.

1) people are profit maximizers.
2) law of diminishing returns (eventuall) kicks in (MC rises)
3) law of demand applies. That is, people purchase more at lower prices than at higher prices. (MR is flat or declining)

If you are in the business of making widgets and you can create a widget for $1 (including opportunity costs) and sell for $2. Of course, your create the widget. As long as the MARGINAL cost of creating something is less than the price, a person/business will continue to create. The business will obviously stop when the cost exceeds the benefit.