Why did Jesus say that "Mary has chosen the better part"?

The Desert Fathers and monastics interpreted this passage as Christ telling us that the contemplative life is the greater portion than the life of the works of mercy.

Mary represents the contemplative life, as she spends all her time listening and taking to heart all that Christ says: in other words, contemplating God. Martha, on the other hand, represents concrete works such as missionary work, helping the poor, and raising a family in faith: in other words, working for the sake of the Kingdom. Both are necessary; both are needed; both are worthy of praise. One cannot exist without the other.

However, the contemplative, due to the nature of his vocation, has loftier choice, because the contemplative is focusing all his energy towards God directly, while the other is focusing energy indirectly: the worker for the Kingdom must focus on God as well as his wife,* his children, his work, etc., which, let's be honest, can distract us from God (the "worker" lives a more worldly life a fortiori, because his focus is on worldly things as well as Spiritual things).

*This is what St. Paul means when he says that it is better for a man not to marry, as he must please both God and his wife.

Christi pax.

Good question.

Though the above answers are excellent, I'll be coming at things from a different direction and with a different perspective.

In Middle Eastern culture, and to a certain extent even today in cultures around the world, the responsibility of hosts is to make their guests feel welcome, accepted, and loved. Although Jesus loved Mary, Martha, and Lazarus and had spent a good deal of time with them, He was still a guest in their house.

Which was more important to Jesus: the cleanliness of the house and what was for dinner, or conversation with His friends and His disciples? Obviously, the latter. I suggest that Jesus, instead of having a big meal with His friends and disciples, would rather have fasted (i.e., skipped the meal) and simply conversed with the people who had gathered in the house.

Remember Jesus' words in John 4:

"But [Jesus] said to [His disciples], 'I have food to eat that you do not know about. . . . My food is to do the will of Him who sent Me and to accomplish His work'" (vv.32,34).

Jesus also said,

"'It is written, MAN SHALL NOT LIVE ON BREAD ALONE, BUT ON EVERY WORD THAT PROCEEDS OUT OF THE MOUTH OF GOD'" (Matthew 4:4).

So, which is more important: bread? or words from God's mouth? Since Jesus was the God-Man, Mary's listening to what He had to say was the "better part," as compared to Martha's distracted serving.

When people get distracted, in effect they are forgetting that "the main thing is to keep the main thing the main thing!" Mary got it; Martha, not so much.

The "better part" of hospitality for us Christians today is to make our guests feel welcome, accepted, and loved. In Greek, the New Testament word hospitality means literally "lover of strangers," which concept has its roots in the Tanakh and its teaching on the responsibility of God's people to care for orphans, widows, and aliens (i.e., strangers). That God was concerned about the aliens in Israel's midst suggests to me that God has the heart of an evangelist who wants aliens/strangers to become part of His forever-family.

In conclusion, the main thing for Jesus was to do His Father's will and to finish His work. For Jesus, this involved preaching, teaching, healing, forgiving, discipling, and ultimately giving His life as a ransom for many. Mary realized this and consequently hung on His every word. Martha, though she may too have realized this, she had forgotten it, temporarily, by allowing herself to become distracted, worried, and upset.

When's the last time you skipped a meal to get to know Jesus a little better and to listen to what He has to say to you? His words proceed from the mouth of God.

Food for thought (pun intended).

Luke 10:38-42 As Jesus and his disciples were on their way, he came to a village where a woman named Martha opened her home to him. She had a sister called Mary, who sat at the Lord’s feet listening to what he said. But Martha was distracted by all the preparations that had to be made. She came to him and asked, "Lord, don’t you care that my sister has left me to do the work by myself? Tell her to help me!" "Martha, Martha," the Lord answered, "you are worried and upset about many things, but few things are needed-or indeed only one. Mary has chosen what is better, and it will not be taken away from her."

Here we have in Mary an illustration of a heart that is given to the Lord and in Martha a heart that is given to pleasing the Lord by works.
Jesus said of Martha "you are worried and upset about many things”; this indicates that faith in God’s grace was lacking in Martha. The one thing that is needed is “faith in God’s grace” from which eternal service legitimately proceeds.