My husband was diagnosed in April of this year with secondary liver cancer. He had bowel cancer 6 and a half years ago which we thought we had beaten. He too is a very private person and finds it very hard to share his emotions with anyone. In fact he seems to be pushing us, the ones closest to him the furthest away.
The only advise I can give you is be there for your parents. If they want to talk let them, if they don't then don't push it. Don't take it to heart if they snap at you, you always hurt the ones closest to you. Remember it is not really them, it is the frustration and pain, both mentally and physically of dealing with this horrible insidious disease.
My thoughts and prayers are with you.