Because once you do that if your chicks/eggs ever get you just sent pheasants out into the world that could never be pure bred, no matter how much line breeding is done to them, and chances are some one could mistake your hybrid offspring for a pure bred and damage their line too. All the ornamental pheasants wild populations are dwindling, so if we don't who else is going to preserve the pure blood lines? You think China cares to do it?
 
You didn't bother to read that thread I linked you did you?
 
Edit: btw no one is telling you not to do it just what our preference is. Hybrids are typically beautiful birds and it is hard not to love their appearance. Given your situation with the two mature birds of either species I think many people would take the hybrid route, especially given how hard it is to find mature pheasants of any particular breed at any particular time. However think if everyone who got pheasants didn't care about hybridization? it wouldnt take too many years before the lady amhersts goldes and red goldens (some of the most popular types) would be a rare find in their pure form. I personally think a pure lady amherst is one of the most beautiful birds around so I would hate to stop seeing them.