This is the heir. Let us kill him, SO THAT the inheritance may be ours

How did that follow logically?

Luke 20:

1 One day, as Jesus was teaching the people in the temple and preaching the gospel, the chief priests and the scribes with the elders came up.

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That's the setting.

9 And he began to tell the people this parable:

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A parable is not necessarily a real-life story but one that makes certain points.

“A man planted a vineyard and let it out to tenants and went into another country for a long while. 10 When the time came, he sent a servant to the tenants, so that they would give him some of the fruit of the vineyard. But the tenants beat him and sent him away empty-handed. 11 And he sent another servant. But they also beat and treated him shamefully, and sent him away empty-handed. 12 And he sent yet a third. This one also they wounded and cast out. 13 Then the owner of the vineyard said, ‘What shall I do? I will send my beloved son; perhaps they will respect him.’

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That would not make very good logical sense in real life, but this is a parable. The owner represented God. The son represented Jesus. The tenants represented the chief priests and scribes.

14 But when the tenants saw him, they said to themselves, ‘This is the heir. Let us kill him, so that the inheritance may be ours.’

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They believed that by killing the heir, they could seize control and ownership. They wished. No, that's not logical. It was a flawed and evil thinking.

15 And they threw him out of the vineyard and killed him.

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The parable predicted Jesus' death.

What then will the owner of the vineyard do to them? 16 He will come and destroy those tenants and give the vineyard to others.”

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Others represented the Gentiles.

When they heard this, they said, “Surely not!” 17But he looked directly at them and said, “What then is this that is written:
“‘The stone that the builders rejected has become the cornerstone’?
18 Everyone who falls on that stone will be broken to pieces, and when it falls on anyone, it will crush him.”

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Jesus brought in Hebrew scripture to support his parable.

19 The scribes and the chief priests sought to lay hands on him at that very hour, for they perceived that he had told this parable against them.

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They saw Jesus' points in the parable.

Why would they think that by killing Jesus, they would inherit the vineyard?

No, it did not make logical sense in real life. It was an element of the parable to point out their evil decision.