What's a word for someone who wants to voice opinions but not have them challenged?

Solution 1:

Perhaps dogmatic?

Merriam-Webster: "expressing personal opinions or beliefs as if they are certainly correct and cannot be doubted"

or, upon looking for synonyms for dogmatic, there's doctrinaire:

dictionary.com: "dogmatic about others' acceptance of one's ideas; fanatical: a doctrinaire preacher"

I think self-rightous may fit:

confident of one's own righteousness, especially when smugly moralistic and intolerant of the opinions and behavior of others.