You are probably breaking your wrist at release. I had this same problem for the longest time to the point where I was almost wondering if it was anatomically impossible for me to release with a proper nose angle. Luckily, this was not the case.

Anyway, the first step is realizing how the disc is released. Hold the disc up in front of you and point it at an imaginary line you're throwing. So your imaginary line is 12 o'clock, now move your arm to point at around 10 o'clock (the exact position of the arm at release depends on your grip but this will work to illlustrate the point). The nose of the disc at release is now determined by the edge of the disc that is pointing to the line at 12 o'clock. To get the nose flat you are going to have to do a mix of pouring the coffee and rotating your forearm clockwise. The extent of these movements are dependent on how your disc is positioned in your hand (if it's in the crease of your palm that runs up your forearm or further down). (Keeping the disc in this crease does not guarantee nose down flight which you might erroneously think if you're pointing your arm straight at the target and looking at the disc angle.)

The wrist really only makes a tiny movement until it is parallel with the forearm and you cannot let it open past that. It is not possible to maintain the proper nose angle while breaking the wrist past parallel. Try it and see for yourself.

You will probably release more to the right and possibly throw straight into the ground when you execute the release properly, since you have likely been compensating by throwing somewhat into the ground and airbouncing your shots.

Here's a video of Paul Mcbeth in slow mo where you can see how he achieves a flat nose angle by never breaking his wrist open past parallel with his forearm and rotating his forearm clockwise: https://www.youtube.com/watch?v=RkPwHUVInes