Just before Jesus died, Jesus said to John, “Behold your mother!”

Joh 19:26  When Jesus therefore saw His mother, and the disciple whom He loved standing by, He said to His mother, “Woman, behold your son!”
Joh 19:27  Then He said to the disciple, “Behold your mother!” And from that hour that disciple took her to his own home.

Jesus also said to His mother, “Woman, behold your son!”  Jesus told his mother and John to look upon each other as mother and son.

Why?

Point 1

Mary’s husband, Joseph, is not mentioned, so it was likely he had died, perhaps even before Jesus’ ministry.  As the eldest son, Jesus had the responsibility of caring for his mother.  With His impending death, Jesus wanted to pass on this responsibility.

Point 2

The natural contenders to take on this responsibility, Jesus’ brothers, were not believers at the time.

Joh 7:2  Now the Jews’ Feast of Tabernacles was at hand.
Joh 7:3  His brothers therefore said to Him, “Depart from here and go into Judea, that Your disciples also may see the works that You are doing.
Joh 7:4  For no one does anything in secret while he himself seeks to be known openly. If You do these things, show Yourself to the world.”
Joh 7:5  For even His brothers did not believe in Him.

They became believers after the resurrection.

Act 1:14  These all continued with one accord in prayer and supplication, with the women and Mary the mother of Jesus, and with His brothers.

Point 3

It appears that Jesus’ brothers lived far away in Galilee and that (at that time) John lived in Jerusalem, inferred from, “from that hour that disciple took her to his own home”, John 19:27.

Conclusion

Considering the above points one can surmise that Jesus deemed John, who was a close friend of Jesus and no doubt also Mary, a better choice than His brothers for two reasons.

1. John being a believer could provide spiritual companionship, particularly in this difficult moment for Mary.
2. John living close by could provide physical care and protection for Mary.