Why does it seem difficult to cycle up a steep hill than to push the bike up at the same speed?

A bicycle is unusual among machines because it has a mechanical advantage (MA) of less than one – typically between 1/3 (in low gear) and 1/8 (in top gear). This helps to convert effort to speed but also means that forces acting on the machine are multiplied by the reciprocal of the MA.

 When riding on the level, the forces of wind and road resistance are small so not much effort is needed, but when going uphill the force of gravity, is also multiplied up, making the journey more difficult.

 On steep hills it may therefore become easier to walk or run than to cycle. When you push the bike up a hill you tend to be doing about 4 or 5 kilometers per hour whereas while riding, even slowly it is at least 8 or 9 km/hr. Also while cycling up a hill our legs move at about half the rotational speed involved in walking, which means we will have to put in twice the amount of work.

Mountain bikers overcome this problem by having extremely low gears on their machines.

Cycling in a bike with low gears at 4 km/hr is surprisingly easy, so it need not be more difficult.