Why intuitively does Break-even point $= \dfrac{\text{Total fixed costs}}{\text{Selling price per unit} − \text{Variable cost per unit}}$? p. 100. Accounting: A Very Short Introduction  (2014).
I understand the green sentence beneath, but not the fractional formula for BEP containing CPU in red? What's the intuition for the latter?

Contribution
The ‘contribution’ is the amount that a particular product line helps
towards covering fixed costs and making a profit. The contribution is
measured as: Sales − Variable costs.  This can also be calculated per
unit of production. The contribution per unit (CPU) is:
$\color{red}{CPU = \text{Selling price per unit} − \text{Variable cost per unit}}$
That is, taking the selling price for one unit of production, and then
deducting all the variable costs for that one unit of production,
gives the contribution per unit.
Break-even point (BEP)
$\color{forestgreen}{\text{The break-even point is the volume of production at which the firm makes zero profit.}}$ Therefore, the break-even point is the level at
which all costs (including fixed costs) can be paid for. The formula
is:
$BEP = \dfrac{\text{Total fixed costs}}{\color{red}{\text{Contribution per unit (CPU)}}}$
So, above the break-even point, any extra items sold will generate
profit. Every unit that is produced and sold in excess of the
break-even point will generate profit of the amount of the CPU. The
total profit made is:
Units in excess of break-even point × CPU
If the firm does not reach break-even point, this implies that it has
not yet covered fixed costs and will therefore make a loss. The size
of the loss will be the number of units under the break-even point,
multiplied by the CPU.

The break-even point can be
derived using the formula given above, or by drawing up a chart such
as Figure 15.
Intuitively, the breakeven point is where the volume of sales results in the gross margin (based on the difference between selling price and variable costs per item) exactly covering fixed costs