but I'm not sharing my coffee

The History: As Che Guerava said, the revolution is immortal. He was publicly mourned in cities all over the world. Not by the Cubans who managed to escape. And his story would inspire young activists for generations to come.
The Judge: Ha.
The History: A trendy symbol of rebellion for those who never had to live under his regime. Symbols of revolution may become commodified, but the idea of a more just world remains.
The Judge: Maybe, but I'm not sharing my coffee.
Source: History vs. Che Guevara - Alex Gendler, TED Ed

What does the sentence in bold mean?

Try: "He was publicly mourned all over the world, but not by the Cubans who managed to escape."

The word "Ha!" Is normally an exclamation and gets an exclamation point.

I guess I'll have to get my own coffee. (I would need more context to understand that one ,)

I think he's probably expressing an anti-communist sentiment.

jutfrank said:

I think he's probably expressing an anti-communist sentiment.

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Thank you, jutfrank.

Does "my coffee" imply "my property?"

WilliamTaft said:

Thank you, jutfrank.

Does "my coffee" MEAN "my property?"

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I want to know myself how that works.

Thank you, Tarheel.

Is the use of "imply" incorrect in this context?

WilliamTaft said:

Does "my coffee" imply "my property?"

Click to expand...

I'm not sure what you mean.

WilliamTaft said:

Thank you, Tarheel.

Is the use of "imply" incorrect in this context?

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It depends. Does it say that or does it hint at it? Can you imply something without using a sentence?

WilliamTaft said:

Does "my coffee" imply "my property?"

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You're asking the wrong question. Of course it doesn't imply that. It says "coffee" so anything it implies must involve coffee. A better question would be "Does using "my coffee" imply/suggest that I'm trying to emphasise that the coffee is mine, not someone else's?