Our denial of him being insane would be because of his systematic actions. Examples would be when the author wrote"Oh I moved slowly,slowly so that the old man did not notice me." In this Sentence it can tell that he perfectly planned his plan. As a sane murderer would do he lied to the police and got guilty.
plotting, planning and subterfuge proved he knew he was committing a crime.Some evidence would be "Now look how I went about it - with caution."Evidence-"Every night at midnight I unlatched his door and once I made an opening wide enough:I moved in slowly."This is a very carefully planned plan for a man with hypersensitivity.