Why is the marginal revenue for a monopoly lower than its price?

The question assumes that marginal revenue is always less than the unit price. This is not true. As a matter of fact it is nor right to even compare the two as the two refer to quite different things. It is like comparing speed with distance.

Please note that price is specified as money or dollars per unit of product, just as speed is expressed as distance per unit of time. In comparison revenue, including marginal revenue, is measured in terms of just money or dollars, just as distance is specified in some unit of distance such as meters.

Further, please note that for the same change in price, the marginal revenue can be positive, negative or zero depending upon price elasticity of demand. The marginal revenue increases with increasing elasticity of demand. With elasticity of less than 1 the marginal revenue is negative, and with elasticity more than 1 the marginal revenue is positive, and keeps on increasing with increasing elasticity. When elasticity is zero, the marginal revenue is also zero.