Have you ever gotten anything big enough in your eye that you had to have a medical person remove it? I got a piece of hot metal that went through the air vent in my safety glasses and landed in my right eye. It hurt like crazy and I could not see a thing. The eye was sore for a few days after the emergency room doctor took the piece of metal out.
Jesus warns us about the hypocrisy of seeing the speck in another person's eye when we cannot see the log in our own eye. It is too easy for us to magnify another person's sin without seeing our own. We want to address their problem before dealing with our sins and faults. It does not work. That is why Jesus tells us to deal with our sins and guilt before trying to deal with the other person.
When we see our own sins and repent, we can confess our sins to God and ask Him to forgive us. That helps us to see our part in the problem, our role in the strained or broken relationship. Then we can admit our part in the problem and work with the other person to resolve them. We can't see very well when we are wearing sin stained glasses.