Theory:

     I had to confess he was right. In less than five minutes he had the gear-case in two pieces, lying on the path, and was grovelling for screws. He said it was always a mystery to him the way screws disappeared.
 
     Common sense continued to whisper to me: ‘Stop him, before he does any more mischief. You have a right to protect your own property from the ravages of a lunatic. Take him by the scruff of the neck, and kick him out of the gate!’
 
     But I am weak when it comes to hurting other people’s feelings, and I let him muddle on.
Explanation:
 
What the man claimed had indeed turned out to be true. In less than five minutes, and before the narrator could dissuade him, the man had the gear-case in two pieces. Moreover, to make matters worse, he lost the screws. Once again, he then started crawling over the garden, and this time to look for the missing screws. He said he found it a mystery when the screws kept disappearing.

The narrator knew that it was high time that he had stopped the man. Common sense told him that he has to put a full stop to the repair work before the man destroyed the cycle beyond repair. As it is, the cycle was in two pieces, and the narrator didn't want to see things getting worse.

The inner voice asked him to take the man by the back of the neck and kick him out of the gate. He was a mad man, and the narrator had all the rights to protect his property and belongings.
 
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The narrator's common sense asked him to push the man out

But as evident from the narrator's inactions, he is a soft-spoken person and is constantly worried about hurting people's feelings.

Hence, he let the man mess with his bicycle.
 
Meanings of difficult words from the paragraphs:
 
Sl. No.
Words
Meanings
1
MischiefHarm or trouble caused by someone or something
2
RavagesThe destructive effects of something
3
LunaticAn extremely foolish or eccentric person; a crazy person
4
Scruff
The back of a person's or animal's neck
4
MuddleBusy oneself in an aimless or ineffective way; turn something untidy
Reference:
National Council of Educational Research and Training (2007). Honeycomb. A Bicycle in Good Repair (pp. 126-132). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.