Surfing is not all about learning how to stand, it is about understanding the ocean and learning how to catch a breaking wave as it transforms from a swell to a wave. If you can master this - standing up is a mere formality.
The surfing skill comes from watching and understanding a wave as it breaks, so you can position yourself in the perfect area to catch the wave, and then accelerate your paddling at the correct time to move down the face of the wave. Once you have mastered this you will have a split second to move your hands into the correct position to adjust your weight back - without falling off the wave (this is why learning on small boards is so much easier).
From here you learn how to catch the wave as it breaks (the thrill of coming down the face of a wave is unforgettable). Through learning all the above skills - you have naturally progressed to a stage where you understand how to safely stand up at the crucial stage of "catching a breaking wave". Your hands are positioned correctly, your weight is distributed correctly and you then notice that due to the downward angle of the surf board, standing up and surfing will become a much easier prospect.
Advancing skills by learning how to surf the wave across the face is the next step, finally - body surfing and surf negotiation without a surf board.
With these skills plus extra skills learnt in body surfing - you have developed the required confidence to allow you to continue learning to surf within your own comfort zone.
Happy Surfing!