Lorraine: Your father kissed me for the very first time on that dance floor. It was then I realized I was going to spend the rest of my life with him.
This line is, of course, followed by a laugh which likely made Lorraine instantly regret the entire thing. Nevertheless, she believed that she knew immediately that it was her destiny to live out her remaining days with Mr. George McFly. Almost as if she had been trapped, relieved of her free will in the matter.
Doc: Marty, I'm sorry, but the only power source capable of generating one point twenty-one gigawatts of electricity is a bolt of lightning. Unfortunately, you never know when or where it's ever gonna strike.
How convenient. A little too convenient. In fact, this fine bit of happenstance may be a major argument in the pro-fate camp. What are the odds that Marty would have gotten—the day before, mind you—information about when a bolt of lightning would strike? Seems a little written in the stars, doesn't it?
Doc: Marty, that's completely out of the question. You must not leave this house. You must not see anybody or talk to anybody. Anything you do could have serious repercussions on future events. Do you understand?
Oopsies. Too late. But Doc clearly understands the negative consequences that could come out of messing with the past. Maybe he should have thought about that before he invented a time machine.
Doc: Please, Marty, don't tell me, no man should know too much about their own destiny.
This pretty much sums it up. Even if there is information that Doc might deem valuable, nay, life-saving, he still doesn't want to know it. Luckily, he changes his mind about that later.
Doc: No, Marty, we've already agreed that having information about the future could be extremely dangerous. Even if your intentions are good, they could backfire drastically. Whatever you've got to tell me I'll find out through the natural course of time.
Here Doc focuses on the "intentions" part of it. He recognizes that Marty wants to do good by divulging information about the future, but there's a divide between intent and reality. He knows that no good can come of it… until he does a little re-evaluating after ripping up that note.