Meaning of "snatch the words from"

What is the meaning of "snatch the words from" as in this sentence:

79. I have seen a religious who used to snatch the words from his superior’s lips, but I despaired of his obedience when I saw it led to pride and not to humility.

Source: St. John Climacus’s The Ladder of Divine Ascent (composed c. AD 600, translated in 1959) page 23

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Another example, but I’m not sure whether the meaning is the same:

Here are the things you shouldn’t miss about school because they, most certainly, didn’t promise you a good time.

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BEING THE CENTRE OF A RUMOUR

Everyone read the fiction based on you that someone sent to the school yearbook. It seemed like reality to them. They roasted you and even remembered you because of that very rumour. Some even got a bad first impression. You encountered them, trying hard to snatch the words from their mouths but that only made the rumour seem truer.

Source: Things you shouldn’t miss about school from The Daily Star Oct 11, 2018

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Third example:

Pamela that next morning might have been the heroine of that almost forgotten "Spenserian" poem of Springtime—"The Gay Lady of Surprise." She opened the door to Martin herself, followed by Leida, carrying her modern suit-case. She walked down the stairs, her hands extended, her eyes dancing, colour on her cheeks—the very spirit of happiness in her walk.

"Confess now that I am an amazement, Martin," she cried, as she took his hands and, leaning over, kissed him lightly on the cheek. "Here I am, with no lines under my eyes, no signs of a sleepless night. You should tell me, indeed, that I am the very holiday lady of your dreams."

"Of course," he grumbled lightly, "if you are going to steal all my favourite phrases and snatch the words from the lips of my favourite poets, you will have to be content with a dumb lover."

"I should be content with you for my lover, dear Martin," she assured him, "however dumb you might be. The vital question is this. Is this forth-coming adventure to be a pilgrimage, a picnic, or an expedition?"

Source: Chapter XV of The Man Who Changed His Plea by E. Phillips Oppenheim, 1942