In Journey to the Center of the Earth, why does Axel not want to go on the trip?

Axel does
not want to go on the trip because he is, in a word, frightened. The journey seems to him to be
fraught with danger, what with having to go inside a volcano (albeit an extinct one) and deep
underground.

Axel conveys his emotions vividly as he ineffectually attempts
to persuade his uncle Lidenbrock to turn back. However, Lidenbrock is inexorable. He is eager
and willing to take any risk in his pursuit of scientific exploration. Indeed, he behaves as
though there were no risks at all, for example when he refuses to take along enough water for
the journey, counting on underground springs to see them through. Axel is dismayed at
this:

The fears I had expressed as to the quality and
temperature of these springs, and indeed as to their existence, had been totally disregarded
(chapter 11)

Lidenbrock, then, refuses to listen to Axel,
the voice of reason. Axel is taken aback at such a dismissive attitude, and his fears are borne
out in this case when they nearly die of thirst at one point during the journey.

His uncles irresponsible attitude increases Axels qualms about the whole expedition.
However, Axel learns how to face up to his fears and sees the journey through to its
unexpectedly successful conclusion. Indeed, he, his uncle and their accompanying guide Hans all
return as heroes.