Tobias,
A sharp straight razor will slide with the grain and remove the stubble easily. It's no different to using a throwaway razor. Sharp is the same cutting feel as a throwaway razor. That's a benchmark for you. It will cut with no soap or water. However with good preparation, it will slide through the stubble with ease, even better than a throwaway.
Against the grain, "the technique thing" becomes more critical. There is a point when you hit the hair were you instinctively know if the blade is sharp enough and if you push a bit, all will be alright. The thing with a straight, is if the angle isn't less than 30 degrees, the blade will cut you. With the throwaway, the angle has to be correct or the blade just misses your stubble altogether. For this reason, people shave with more confidence with a throwaway.
But from what you said, the blade you had was not sharp enough. It should not skip over stubble if you were running the blade on your skin.
If you ran your finger across the blade or did anything to check the sharpness, maybe you are to blame. It is so easy to take the sharpness off the edge of a straight razor that until you understand the process, it's hard to believe.
If all you did was prepare, open the razor and shave then the razor was not sharp.
Only you can answer the question, but I know from when I started, I often would blame anybody but myself for playing with a blade that is anything but a toy and has to treated so carefully that learning to do this is in itself an art.
Once you understand all this edge stuff, it's easy because you know what to do if the blade needs a quick strop or touch up hone. Both exceptionally gentle techniques to put right a razor that has usually been treated roughly.
Whatever, stick at it, it's worth it in the long run. Honest.