Why do the Mentos blow up in the coke?

Menthos does "blow up" with Coke. It would do the same with any carbonated drink. The reason a carbonated drink container may be seen to erupt in a fountain of bubbles is due to the rapid release of carbon dioxide. The release is due to small roughness on the Mentos' surface causing gas bubbles to "seed" and the formation of bubbles to proceed rapidly. Rapid release of Carbon Dioxide will cause bubbles and an increased pressure and resulting blow up.

It is worth adding a comment about the Mentos hoax around the internet.
The action has nothing to do with chemical reactions but is a physical process. It doesn't pose risk to person who consumes Coke with Mentos. Fizzing is normally felt in the mouth when drinking Coke and is sign of the carbonation releasing carbon dioxide from the drink. The addition of Mentos speeds up the process and would not do any harm from the gas itself. Of course, one may imagine an extraordinary circumstance where someone would finished the whole bottle of carbonated beverage without burping and with all gas still in liquid. For such case, dropping Mentos down the throat while sealing the mouth might pose a threat. (It is unimaginable that someone would go that far for such self torture). The danger of Mentos with Coke is a hoax. See related link.