Monopsony diagram curves Why is the marginal cost curve not the same as the supply curve?

My personal explanation is that since the marginal cost curve is cost of producing each new product, the supply curve just represents the break even point of selling a certain number of these products. The seller can sell some at a profit, and some at a loss, and as long as the loss and profit cancel out, he's on the supply curve. Thus the supply of producing x goods is just the average of the marginal cost curve from 0 to x.

This explanation seems logical to me, but I have been given an alternative explanation - the supply curve is that of the market, whereas the marginal cost curve is intrinsic to the firm. However, I am unsure as to why the market supply would be related to the marginal cost curve as the average of its integral.
There are two assumptions in your explanation that require change

1st of all, regading the seller


  The seller can sell some at a profit, and some at a loss, and as long
  as the loss and profit cancel out, he's on the supply curve.


The supply curve theoretical logic is that the seller will produce as much products as possible, at a rising cost, as long as the market price that he sees is higher than the last product he produced - the marginal product
Based on that, the seller will always sell at market price. the profit comes from the gap between the market price and the entire cost of production, which is cheaper than the marginal cost. he's initial products cost less

The supply curve is the average MC of all firms, which, in a competitive market model, share the same technology, since open information is available, so the average should be of identical firms