Which two of the three statements is true?

[Eddygp]

Person 1: I like bananas. I like fish. I like owls.
Person 2: You like owls and fish.
Person 1: No, keep trying.
Person 3: You like fish and bananas.
Person 1: Correct!
Person 3: I drank seawater on purpose. I like owls. I have three eyes.

And so on...
I start:

I play the French horn, the piano and the violin.
I have drunk cola mixed with chickpeas.
One of the previous statements is false.

[new guy1]

I will take a guess and say that the cola mixed with chickpeas is false... unless you are including the "one of the previous statements is false" in a list of three, then the first two are true

[Votanic]

It is indeed tempting to guess that

One of the previous statements is false.

is in fact, the false statement, ...but unless the OP were to make an unlikely return appearance to this thread, the rest of us will never know with certainty.

I'll go next.

I've stood atop Ayres Rock.
I've eaten an entire scorpion.
I like anchovies on pizza.

[Rosenbaum]

Person 1: I like bananas. I like fish. I like owls.
Person 2: You like owls and fish.
Person 1: No, keep trying.
Person 3: You like fish and bananas.
Person 1: Correct!
Person 3: I drank seawater on purpose. I like owls. I have three eyes.

And so on...
I start:Block Blast

I play the French horn, the piano and the violin.
I have drunk cola mixed with chickpeas.
One of the previous statements is false.

If statement 3 is true, then one of the other two must be false. If statement 3 is false, then both statements 1 and 2 are true. So we have two cases:
If statement 3 is true, then either statement 1 or statement 2 must be false.
If statement 3 is false, then both statements 1 and 2 are true.
So the two correct statements are:
I play the French horn, the piano, and the violin.
I drink cola mixed with green beans.