Incorrect, if your brothers (assumption) thought you were nuts (assumption again), and you died a criminal, that still doesn't mean that it's ok to leave the care of your widowed mother to a friend rather than to them
It's not "nice" NOW and then it would have been something a religious Jew like Jesus would never do.
So, Jesus telling John to take care of Mary as his Mother tells you that He had no other brethern with Mary as their mother.
His ... brothers ... were ... not ... there.
Jesus gave John the job because His brothers were not there, Jesus was the oldest, it was His responsibility to ensure His mother was cared for. He chose someone He trusted, someone who believed in Him, someone who was there ... that was John.
No, it doesn't. It tells us that Jesus did not think them able to care for Mary, their mother. They could have been too young, too rash, too unbelieving. His brothers probably were miles away from the crucifixion. They came to belief late.