Why is bench pressing your bodyweight harder than doing a pushup?

While doing push-ups, you don't push your whole body weight. You have your toes on the ground, so your body weight is distributed between your feet and your arms.

While benching, you have no support from feet. You hold the whole weight with your arms, so benching your body weight is always tougher.

It's harder because you are benching more weight. Benching your bodyweight requires your upper body to complete 100% of the lift.

When your feet are on the ground and you are pushing yourself up you are only lifting approximately 1/3 of your body weight. You should be able to do much more push-ups than repetitions of your weight on the bench press.

Consider this, is it easier to get off the couch or squat your body weight? The answer has the same basic principle, the more an object weighs the harder it is to lift.

Consider leverage. Assume as in @Michael's comment that the centre of mass is somewhere near the middle. Further assume that the toes are fixed to the floor. If the torso and legs are rigid the centre of mass does not lift as far as the shoulders (at which the pressing force is exerted), so you've got leverage in your favour. This probably reduces the lift to about 2/3 or 3/4 of what it would be if you didn't put any weight on your feet.