If you have your own faults, don't judge others based on their faults.
1. People in glass houses shouldn't throw stones
This is mainly about starting fresh. A newer broom (a fresh start) will sweep cleaner (give a beter result)
2. A new broom sweeps clean
3. Empty vessels make the most noise
For a dog to bite you, you need to get close enough to get a hair off of it.
4. A hair of the dog that bit you
Basically the results (smoke) tend to lead towards a likely cause (fire).
5. There's no smoke without fire