Theory:

Tabaqui: My Lord, my Lord, it went in here!

Father Wolf: Shere Khan does us great honour, (angrily) what does he need?

Shere Khan: My quarry. A Man’s cub went this way. Its parents have run off. Give it to me.

Narrator: Shere Khan had jumped at a woodcutter’s campfire, as Father Wolf had said, and was furious from the pain of his burned feet. But Father Wolf knew that the mouth of the cave was too narrow for a tiger to come in by. Even where he was, Shere Khan’s shoulders and forepaws were cramped for want of room as a Man’s cub would be if he tried to fight in a barrel.

Father Wolf: The Wolves are a free people. They take orders from the Head of the Pack, and not from any striped cattle-killer. The Man’s cub is ours – to hunt if we choose.

Shere Khan: What talk is this of choosing? It is I, Shere Khan, who speaks!
Explanation:
 
We see Tabaqui being quite servile* when he addresses Shere Khan as 'my lord'.
 
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Tabaqui and Shere Khan

Tabaqui's evilness and sly character becomes evident when we hear him tell the tiger that the Man's cub had gone inside the cave. From this, it is quite apparent that Tabaqui was not a friend and well-wisher of the wolves. Though Tabaqui informed the wolves about Shere Khan’s arrival, he didn't do it out of good intention.

Father Wolf was angry at his visitors. His tone was filled with contempt when he enquired the tiger why he had come to the cave. One could note that the wolf didn't even bother to address the tiger directly. In the line "what does he need?", it could be observed how 'he'- the tiger- was merely considered as a third person.
 
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Father Wolf growls at his visitors

Shere Khan was equally furious and wanted his prey back. The tiger ordered the wolves to return the Man's cub. We also learn that the little boy’s parents had escaped, and the tiger would have to get his hands on the boy to satisfy himself. To make matters worse, the tiger had hurt his feet when he jumped into the woodcutter's fire. Hence, Shere Khan was definitely in a bad state. He was furious, embarrassed, annoyed, and in pain.

So, why do you think the tiger was asking the wolf to return the boy? Obviously, the tiger was stronger than the wolf. He could quickly put up a fight with them. So, what prevented the tiger from reaching out and picking up the Man's cub?

The cave. Yes, the cave was too small for the tiger to enter. Shere Khan was stuck where only his head, shoulders, and forepaws could get inside the cave.
 
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The cave was too small for the tiger to enter
 
The writer also compares the cave to that of a barrel. The cave was to the tiger what a barrel would be to a human.
 
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A barrel

Coming back to the play, we see that Father Wolf was quite unhappy with the tiger ordering them around. He retorted back by reminding the tiger that the wolves were free people and never took orders from anyone besides their pack leader. Moreover, we see Father Wolf mocking the tiger by calling him a 'striped cattle-killer'. The wolf also added that the Man’s cub belonged to the wolves to hunt when they choose.

The wolf must have rubbed the tiger's ego, for the tiger responded by saying that choosing was never an option for the wolves. He also added the statement, "it is I, Shere Khan, who speaks!", exhibiting the pure arrogance he had in him.
 
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Shere Khan wanted to eat the Man's cub but couldn't enter the cave
 
Meanings of difficult words:
 
S. No
Words
Meanings
1
My LordA lord is someone who has a lot of power in a particular area; 'my lord' is a respectful form of address used to nobleman or to people holding the highest ranks
2
QuarryAn animal, bird, or fish that is hunted, especially by other animals; prey
3
FuriousExtremely angry
4
Narrow Having a small distance from one side to the other, especially in comparison with the length
5
ForepawsThe front feet of most land mammals
6
Cramped Not big enough for the people or things in it
7
For want of room In need of space
8
BarrelA large, round container for storing liquids or food
9
Free peopleA democratic setup where people (or animals) are not controlled by an outside force; here, the wolves are not ruled by the other greater beasts like tiger, but rather by the head of the pack 
10
Striped cattle-killerReference to the tiger (as a mockery); 'Stripped' refers to the appearance (the black lines found on the tiger skin), and 'cattle-killer' describes the tiger's hunting style
11
Servile*Having or showing an excessive willingness to serve or please others
Reference:
State Council of Educational Research and Training (2019). Term-3 English Standard-6. The Jungle Book. (pp 116 - 121). Published by the Tamil Nadu Textbook and Educational Services Corporation.