This can be explained by using the concept of energy. At the perigee, a satellite's gravitational PE is a minimum because it is closest to the planet, and thus its KE is a maximum. Consequently, the satellite's speed is the greatest at the perigee. At the apogee, a satellite's PE is a maximum because it is farthest away from the planet, and thus its KE is a minimum. As a result, the satellite's speed is the least at the apogee.
PE is energy due to the relative position of two interacting objects.
At the apogee, a satellite's gravitational PE is a maximum because it is farthest away from the planet. At the perigee, a satellite's gravitational PE is a minimum because it is closest to the planet. A wrench dropped from a high-flying jumbo jet also has the tangential speed of the jet, but this speed is insufficient for the wrench to move around the earth. Instead it falls onto the earth. Besides, the jet is still in the atmosphere and the air resistance would slow down the tangential speed of the wrench.