I really did believe that I was a lousy short putter. And a funny thing about belief is, it often proves to be true. Add that bit of negativity and doubt to your stroke when trying to hole a three footer and you'll miss a bunch of them.
Bobby Jones addressed this issue in his book Bobby Jones on Golf. When speaking about the sort of attitude you wanted to cultivate on the greens, he wrote:
"It is worthy of observation that nearly everyone finds it easier to stroke properly putts of twelve to fifteen feet than those from less or greater distances. There is a very good reason why this should be true. The player fears he will miss a shorter putt, and fears he may fail to lay a longer one dead, but when he is putting in the middle distances, he merely hopes he may hole out, without feeling that he must guide the ball into the hole--and he knows that he will not likely take three putts.
We would all profit greatly if we could cultivate this attitude toward putts of all lengths; it ought to be easy, too, for we all know, or should know by this time, that worry does very little good. If we must be wrong, we may as well make our mistakes gracefully by choosing the wrong line as by allowing a nervous, overcareful stroke to pull the ball off direction."
I think this is the one thing I've actually improved upon with age. By taking this advice, and looking at every putt the same way, be it three feet or thirty, I now make more putts; and suffer less when I miss them. You are not supposed to make every putt. Even great putters miss the odd short one. There are so many things that can go wrong, even over three feet of imperfect turf. So, why not just stand up there, put your best stroke on it, and if it decides to miss just "let it go hang," as Bobby wrote.
Putting can drive you crazy. But it doesn't have to.