Push-ups call on a lot of muscle, and that muscle working together, so any weak link in the chain can make them too hard to do.
Some things that might help:
As honeybunch mentioned, core strength is important, so just practicing planks can help strengthening the muscles used in push-ups in a static way. Start with "on the elbows and toes" planks : set a timer for 2 minutes, and do as many as necessary in that time, going down to knees only when necessary, and only as long as necessary. When you feel your back rounding or (more likely) sagging, pull in on the core and try to hold good position a bit longer. You may shake, but hold on!
Then, when you can do the whole 2 minutes in one plank, progress by going to the hands. Then try lifing one leg at a time.
When doing push-ups, instead of doing "on-the-knees" versions (which aren't an easy transition to the "on-the-toes" ones), do them all with a straight body, but change the level of your hands as necessary, to take weight off the front of the push-up and make it easier. (I think this trains the body to work in the plank/pushpup position better than going from the knees to the toes push-ups).
From easier to more difficult, height progressions can be: hands on wall, hands on kitchen counter, hands on bathtub rim, hands on kitchen chair seat, hands on step platform set at 12", then 10", then 8", then 6", then the platform itself (4"), then the floor.
YOu can also do a different type of progression, as Honeybunch does, and do the moves off a stabilty ball, starting with ball under hips, then ball lower down on thighs, then ball right below knees (not ON the knees), then ball on shins, then toes on ball. Though this does make more of a decline push-up position.
Try negative push-ups: Get into the top position for a push-up,, lower down sloooowly, holding at the 'sticking point" if you can, then go to knees and pushpup in the 'on-the-knees" position. Once at the top, go to toes and lower down again.
Give yourself enough of a break between sets of push-ups to fully recover (ie: don't try to do the push-ups in GS chest/triceps 'as-is").
When prepping to do a push-up, widen your back and chest, spread your fingers.
Try to think of this in a positive way: if something is hard for you, so much so that you hate doing it, it's probably something that you need to work on (it indicates a weakness) and will benefit you in the end.