Many people that are of various religious beliefs like to use the verse about a log in your eye and a speck in your brothers eye. Most of the time this is used to say that nobody is perfect, we all have our own problems, and go away and deal with your own problems and leave me alone. It tends to be used towards people that they see as being presumptuous.
Matthew 7:3-5King James Version (KJV)
3 And why beholdest thou the mote that is in thy brother’s eye, but considerest not the beam that is in thine own eye?
4 Or how wilt thou say to thy brother, Let me pull out the mote out of thine eye; and, behold, a beam is in thine own eye?
5 Thou hypocrite, first cast out the beam out of thine own eye; and then shalt thou see clearly to cast out the mote out of thy brother’s eye.
The speck in the brothers eye compared to the log in your own eye is meant to say that when you have large issues of your own to contend with, you have little room to speak on the same subject as someone who does not have very much issue. This does in no way mean not to tell your brother when you see there is an error they do not see that would be of great use to them. You are helping them to avoid logs, not specks.
An example of driving a car should be a useful analogy.
You help the driver avoid crashing into the car in front of you if they nodded off to sleep but don’t annoy the crap out of the driver by backseat driving when all you were telling them is when to stop and go and where to turn and how fast to drive and how to drive in general.
It has a useful application in groups that want to blame each other for failures. We all fail at least a specks worth of failure. Not all fail with a logs worth of failure. It allows all parties to see that they too are fallible (capable of failure).
Another meaning can be pulled from this set of verses which relates to altruism and helping people. You cannot very well help anyone else unless you are first capable of doing such a thing. If you are without room to have people stay with you, then they should not stay with you as then you both are now in peril.
This does not mean do not help others, but it means if you have a log worth of problems, do not start taking on other peoples issues until you have contended with your own to a sufficient point. If you have little issues to contend with as we all do, then you can help. If you have a heap of problems that someone else would be best helping you instead, then do not take on someone elses problems that will only serve to make you be unsustainable.
An example of this is if you do not know how to swim, you don’t want to try to save someone that is drowning or you now will be drowning and make it harder to save the people drowning as there are now more than one of them. It is sad that you cannot help at times but it is necessary to survive or you can do nothing to help any further.