It's not out of the context, what's wrong with you? :|
You explained nothing. You just presumed some things.
Tsunade's body in general and ninjutsu is far more complex.
And she didn't use it because she had the antidotes done? :|
She used it before with Kankuro, why is so hard to think?
1) Lets read it together. Chiyo acknowledges Tsunade better in med jutsu so then she goes ahead and says this "
"During THE Great War"
Meaning there was a war that happen, which once obv the 2nd ninja war.
Chiyo then adds
"..." applying a long story of the event in the war. But what happens during wars? Nations fight nations. Ninja's fight ninjas, there is no soloing during wars unless it applied in context. So far the context doesn't mention anything about soloing/vs soloing.
"She was able to figure out the poison(s) I created"
Meaning more then one. Now use Who? What? Where? How? and Why? in this statement. She is clearly talking about the war the they both were in. Chiyo eventually has to fight the fire village. Some of them are bound to fight in the air and get poisoned.
"And mix antidotes immediately, which embarrassed me"
Now how to you MIX antidotes? Come on, common chemistry. You have to first KNOW the source of the poison THEN you have to find EACH INGREDIENT part to Counterpart the effects of poison. Tsunade can't know someones "secret poison" already prepare. Take the Kunkuro's situation when he was poison for an example.
So yes you are taking it out of context.
2). To remove poison out of your system took time. Why would Hanzo wait for Tsunade to establish to carefully remove the poison. This leaves her open more matter how good she it. But I like how this jutsu does take care of the poison from staying.