You would not be covered by local health insurance in the EU country you will visit solely on the basis of citizenship. EU-wide coverage is based on reciprocity (if you are insured in one EU country, then you are covered, under certain conditions, during visits to the others) but you need to qualify in the first place and that typically requires being a resident and having the right kind of insurance.
At the same time, you don't “need” to buy health insurance if you don't want to. Purchasing insurance is mandatory for visa holders and, in most places, for residents but as an EU citizen you are allowed to visit without health insurance. That's really up to you.
Don't forget that your regular health insurance, if you have one, might cover emergency healthcare costs abroad. It's different from a proper travel health insurance in that it typically would not cover medical evacuation or the difference between local prices and healthcare costs back home but it would typically cover at least some of the expenses in my experience.
Finally, for completeness' sake, note that there are also bilateral agreement through which countries afford some coverage to citizens from the other country. Those are typically negotiated at the national level (not the EU level) and I am not aware of any with Brazil but such agreements do exist (for example, the NHS has a list for the UK).
